Question

1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5)

[* for a. the answer that I obtained was
y-5 = -1/18 (x-3) ]

b.) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?

c.) Find equations for the tangents to the curve at the points where the slope of the curve is 18.

Answer 1

a) correct
b) smallest slope ---> minimum slope
so set derivative of slope = 0
that is, the 2nd derivative = 0 and solve

c) set 3x^2 - 9 = 18 and solve
You will get two differenent x's, find the matching y's and do the usual thing to find the equation.