anonymous 3 years ago 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)

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

plug stuff in, solve for x

5. anonymous

what does that equation say?

6. anonymous

is that slope equation?

7. anonymous

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

8. anonymous

how do i use this to get the x coordinates

9. anonymous

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

10. anonymous

oh ok thanks

11. anonymous

sure!