derivatives of polynomials and exponential functions

Question

Find all points (c, f (c)) on the graph of f (x) = x3 − 3x2 where the tangent line has slope 9.

Answer 1

f(x) = x³ - 3x²

f'(x) = 9 So, 3x² - 6x = 9.

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0 x = 3 or -1

Points on the graph of y = f(x) where tangent line has slope 9 are (3, f(3)) and (-1, f(-1)).

(3, f(3)) = (3, 0)

(-1, f(-1)) = (-1, -4)