Question

find the x-coordinate of all points on the curve y=36xsin(17x) + 306sqrt3(x^2) -33
domain pi/34 < x < 3pi/34
where the tangent line passes through the point (0, -33)(not on the curve)

Answer 1

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

Answer 2

answers are x1 = 5Pi/102 and x2 = 7Pi/102
i need to know to do get it though

Answer 3

(f(x) - -33) / x-0 = f'(x)

Answer 4

plug stuff in, solve for x

Answer 5

what does that equation say?

Answer 6

is that slope equation?

Answer 7

rise/run =slope

yf-yo / xf-xo = slope of the tangent at (xf,yf)

Answer 8

how do i use this to get the x coordinates

Answer 9

what's f(x)? plug it in.
what's f '(x)? plug it in.

Answer 10

oh ok thanks

Answer 11

sure!