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 one year ago
Find an equation of the tangent line y = f(x) at x = a. f(x) = sin 4x, a = pi/8
 one year ago
Find an equation of the tangent line y = f(x) at x = a. f(x) = sin 4x, a = pi/8

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm I think you've done a few of these types of problems. So I'm just curious, which result makes more sense to you. Seeing our tangent line in slopeintercept form: \(\large y=mx+b\), Or in pointslope form: \(\large yy_o=m(xx_o)\).

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0in slope intercept from

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok we will have 2 pieces we need to find. \(\large m\) is the slope of our tangent line. Take the derivative of your function, and evaluate it at \(\large x=\pi/8\). That will be your \(\large m\) value.

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0when i find the derivative a = pi/8 is not int he equation right?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Take the derivative of sin(4x) first. Don't plug a=pi/8 in until after you've taken a derivative.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1ok good, now plug in x=pi/8 :D

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0i got 0 after i plugged in and solved

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok sounds good. So we've determined that the slope \(\large m\) of our tangent line will be 0. \[\large y=mx+b \qquad \rightarrow \qquad y=0x+b\] Now we just need to find the \(\large b\) value.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1To find it, we'll need to plug in a coordinate pair that falls on the line. Well, since our line is tangent to the curve at x=pi/8, we can plug x=pi/8 into that function to get a corresponding y value. This will be the coordinate pair we'll plug into our tangent line.

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0so i should plug in pi/8 into y = mx + b?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1no, plug it into your original function, before you took the derivative of it.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So that gives us a coordinate pair of \(\large \left(\dfrac{\pi}{8},\;1\right)\). Plug that into your tangent function to solve for \(\large b\).

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0ok so y = 0x + b so i should plug it in place of b?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1No, your coordinate pair is \(\large (x,\;y)\). Plug it into those.

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0okay so 1 = 0(pi/8) + b

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So what is your b value? :3

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok sounds good. So if we plug that missing \(\large b\) into our tangent line equation, we get,\[\large y=0x+1\]Which can be simplified to,\[\large y=1\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I guess it's really 3 steps. We had to find ~\(\large m\) ~\(\large b\) ~A Coordinate Pair.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1It's not too difficult, just a lot of silly letters :) Keep practicing!

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0okay so our equation is complete? and yes just lot to do and thanks

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that's our final answer.
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