g′(x)=7x^2−8x+7 When is the function g(x) concave down?

Question

g′(x)=7x^2−8x+7 When is the fuction g(x) concave down?

Answer 1

A function is concave down when its second derivative < 0. The second derivative of g(x) is the derivative of g'(x) so g''(x) = (7x² - 8x + 7)' = 14x -8

To find when g'' < 0, set 14x - 8 < 0

14x < 8

x < 8/14

So g(x) is concave down when x < 8/14