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mathcalculus
 2 years ago
PLEASE HELP :( !!
y=13e^(3x^2)6x
at x=3 in the form y=mx +b has
mathcalculus
 2 years ago
PLEASE HELP :( !! y=13e^(3x^2)6x at x=3 in the form y=mx +b has

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mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0f'(x)= 78xe^(3x^2)6

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0slope= 234e^276 y=13e^2718

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2So you're looking for an equation of the line tangent to the curve f(x) at x=3?

akotto4897
 2 years ago
Best ResponseYou've already chosen the best response.0omg this is so simple

akotto4897
 2 years ago
Best ResponseYou've already chosen the best response.0wat is america coming to

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes, Determine the equation of the line tangent to the graph of

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah but I'm not sure why I'm getting this wrong.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2@akotto4897 wtf is wrong with you? Why would you call someone elses problem `so simple`. It's like someone in 5th grade calling 3rd grade math SUPER EASY! Just because you understand it doesn't mean that everyone else is on your level...

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Ok that's enough of my rant :) lemme check your work a sec :3

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0lol, i appreciate that. but yes, let's begin.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Mmm ok so your slope looks good. So what coordinate pair are we using to find our yintercept?\[\Large f(3)\quad=\quad 13e^{27}18\]Mmm ok ok I see you have the written down already :3 \[\Large y_{\tan}\quad=\quad mx+b\]So if we plug in our coordinate pair, we get something like this, yes?\[\Large 13e^{27}18\quad=\quad (234e^{27}6)\cdot 3+b\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0woah so the slope is good and the y too.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see there's an x there.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so would it be 247e^2718?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2for your y_tan? or for b?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Hmm after you find your b value, you should plug it back into the \[\Large\bf y_{tan}\quad=\quad \color{royalblue}{m}x+\color{royalblue}{b}\] For our final answer, we DON'T want the coordinate pair plugged in. We're only trying to fill in these blue pieces.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so how do i get to the answer.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0at first i thought it was 247e^27 6x

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2grr sorry website crashed on me >:c

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i just don't understand what to do at the point slope formula.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i keep getting the answer wrong.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\Large\bf y_{\tan}\quad=\quad \color{royalblue}{m}x+\color{royalblue}{b}\]Plugging in our slope,\[\Large\bf y_{\tan}\quad=\quad \color{royalblue}{(234e^{27}6)}x+\color{royalblue}{b}\]Then we plug in our coordinate pair to find b,\[\Large\bf \color{#DD4747 }{13e^{27}18}\quad=\quad \color{royalblue}{(234e^{27}6)}\cdot\color{#DD4747 }{3}+\color{royalblue}{b}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2So we have some 18's cancelling out. And I think we get a b value of,\[\Large\bf \color{royalblue}{b\quad=\quad 689e^{27}}\]Something like that?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0isn't it y(13e^2718)=234e^276x+18

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0right, yy1=m(xx1)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so in this case, slope= 234e^276 y=13e^2718

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2No that's `pointslope` form of a line. yy1 = m( xx1) We don't want to use that. We were told to use the `slopeintercept` form of a line. y=mx+b

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0can we do it the way i had it please?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah but i thought i could use that to find the equation of a tangent line

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0I've been using that for other problems and it worked.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Yes we can use that, so let's see if we can get it set up correctly. Lemme see if I can match what you wrote a sec :)

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\Large\bf yy_1\quad=\quad \color{royalblue}{m}(xx_1)\]\[\Large\bf yy_1\quad=\quad \color{royalblue}{(234e^{27}6)}(xx_1)\]Then plugging in our point:\[\Large\bf y\color{#DD4747 }{(13e^{27}18)}\quad=\quad \color{royalblue}{(234e^{27}6)}(x\color{#DD4747 }{3})\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0after that I'm lost lol

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Ok so now we just need to get in into the form y=mx+b. So we need to multiply out the brackets, then we gotta isolate the y term.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large\bf y\color{#DD4747 }{(13e^{27}18)}\quad=\quad 234e^{27}x6x 702e^{27}+18\]I think it expands like that, yes? Give it a try :)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yup, but i seem to be doing that wrong unfortunately.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0wait don't we just multiply out the 6 and 6*3 only?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, true. We probably want don't want the x's expanded like that,\[\large\bf y\color{#DD4747 }{(13e^{27}18)}\quad=\quad (234e^{27}6)x 702e^{27}+18\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\Large 234e^{27}\cdot3\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0why don't we multiply 234e^27 with x?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large\bf (234e^{27}6)(x3)\quad=\\ \large\bf\quad (234e^{27}6)x(234e^{27}6)3\]And we only want to multiply out the part with the 3.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0im so confused. i do't understand why we did this problem differently than all the others when it comes to this part.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so for (234e^27−6)(x−3) i thought we do foil

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, foiling should give you this,\[\large\bf 234e^{27}x6x 702e^{27}+18\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2Are you not getting that when you foil..?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes i have that! :)

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2We don't want multiple x terms, so we'll factor an x out of each of the first two terms.\[\Large\bf =\quad \large\bf (234e^{27}6)x 702e^{27}+18\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0where does my foiling go?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0great so we factor?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2We had this,\[\Large\bf y\color{#DD4747 }{(13e^{27}18)}\quad=\quad \color{royalblue}{(234e^{27}6)}(x\color{#DD4747 }{3})\]It foiled to give us this,\[\large\bf y(13e^{27}18)\quad=\quad 234e^{27}x6x 702e^{27}+18\]We factored out an x to give us this,\[\large\bf y(13e^{27}18)\quad=\quad (234e^{27}6)x 702e^{27}+18\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2We finish by solving for y.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large\bf y=\\\large\bf (234e^{27}6)x 702e^{27}+18+13e^{27}18\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2the 6 and the 18 are not like terms, we can't combine those.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2I don't know why you insisted on using pointslope form for this one. It seems way more complicated :c

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but it's the only way for me… i have to stick to this or else i'll be completely lost in the exam

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2This one only ended up being complicated because our slope was `2 terms`. So it ended up being a ton of multiplication.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0damn im so confused.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0what would be he answer btw?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large\bf y(13e^{27}18)\quad=\quad (234e^{27}6)x 702e^{27}+18\]From here: you add (13e^{27}18) to each side,\[\large\bf y=\\ \large\bf(234e^{27}6)x 702e^{27}+18\color{orangered}{+(13e^{27}18)}\]Does that step make sense? +_+ That's how we isolate the y term.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2From there we can drop the brackets since nothing in being applied to them, \[\large\bf y=\\ \large\bf(234e^{27}6)x 702e^{27}+18+13e^{27}18\]It looks like the 18's will cancel out,\[\large\bf y=\\ \large\bf(234e^{27}6)x 702e^{27}+\cancel{18}+13e^{27}\cancel{18}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2And the exponential terms ( not the one attached to the x ) are like terms, so we'll combine them,\[\large\bf y=\\ \large\bf(234e^{27}6)x \color{orangered}{702e^{27}+13e^{27}}\] \[\large\bf y=(234e^{27}6)x \color{orangered}{689e^{27}}\]And I think that's our final answer, assuming I didn't make any boo boos along the way.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0wait which is the mx and b?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh it is correct….

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.2\[\large\bf y=\color{royalblue}{(234e^{27}6)}x \color{orangered}{689e^{27}}\]\[\large\bf y=\color{royalblue}{m}x +\color{orangered}{b}\]
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