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\[\frac{ f(x) - (-33) }{ x - 0 }\]

f(x) = \[f(x) = 36xsin(17x) + 306\sqrt{3}x^2 -33\]

x=0

\[\frac{ f(x) - (-33)}{ x-0 } = f'(x)\]

that is the derivative formula at x=0; X=0 is your answer

is it? the answers says that x = 5Pi/102 and 7Pi/102

alright Plug in either 5pi/102 or 7pi/102 in f(x) and see if you get -33.

so im not sure if the rise/run formula is the right thing to do

which is where answer x= 5Pi/102 and 7Pi/102 comes from

alright. let's see if we can write the equation of the tangent line

maybe?

with one m being rise/ivrun and the other m being the derivativer
equate the two toeeach other

dont think it works though

yea the derivative is not defined at 0

i tried doing this but im still not getting the correct answer

did you try getting f'(x), maybe i did it wrong

is the x^2 in the square root?

no

oh, then I was doing it all wrong... let me start over

so take the limit after the rise/run formula after you factor it?

of the rise/run*

yea

this gives you the slope, and then what do you do to get the answer

\[\lim_{x \rightarrow0}36\sin(17x) + 306\sqrt{3}x^2\]

slope equals to 0, and then...?

0 = f'(x)
0 = \[0 = 612xcos(17x) + 36\sin(17x) + 712\sqrt{3}x\]

maybe solving for x here would be the answer?

the answer is 5pi/102

oh did you get it?

and 7pi/102... you took the derivative wrong

oh..

you shouldn't have 712, its 612

what is f'(x)?

ohh

and set them equal as you did before, 36sin(17x)+306(3)^(1/2)x=36sin(17x)+612xcos(17x)+612sqrt(3)x

solve for x, and thats what you get?

\[36\sin(17x)+306sqrt(3)x=36\sin(17x)+612xcos(17x)+612\sqrt(3)x\]

yea, x= (1/102)(12*k*pi+5pi) or x = (1/102)(12*k*pi-5pi)

n is an integer, pick n so that x is between pi/34 and 3pi/34

oh ok, thanks!

np

whats n?

hold on a second I will attach a file soon

what is k?

I used k instead of n; its the same thing

oh ok

when you isolated for k , what are you finding

is that like the period

no; im trying to find k. x should be in a certain range. so if x is between pi/34 and 3pi/34 then (pi/34)

ok i finally got it

thanks for your help!

np...