Question

Determine all the points on the curve

y = 2x ^ 3 + 3x ^ 2 - 18x + 3 where the slope of the tangent line is -6.

Answer 1

$y = 2x^3+3x^2-18x+3$

$y'(x_0) \text{ is the slope of the tangent at the point }x_0$

$y'(x)= 6x^2+6x-18$

$6x^2+6x-18 =-6$

$x^2+x-2 =0$

$x_1=1;x_2=-2$

Answer:$x_1=1;x_2=-2$