If i let f(x) = x3 − 7x2. how do I find the points on the graph of F where the tangent line is horizontal.

Question

and

what is the smaller x value in a (x,y) setting?

and

what is the larger x value in a (x,y) setting?

Answer 1

f(x) = x³ - 7x²

Slope of tangent line is value of x when f'(x) = 0

f'(x) = 3x² - 14x

3x² - 14x = 0

x(3x - 14) = 0

x = 0 or x = 14 / 3