Answer to Question #309166 in Calculus for NURUL

Question

Consider the function, f(x)=2x³ - 24x² -7. Find the intervals of x where f(x) is

increasing or decreasing.

Answer 1

Given , f(x) = 2x³ - 24x² - 7

At the critical point , we know that

f^'(x) = 0

So, differentiate the given equation with respect x

f^'(x) = 6x² - 48x = 0

6x(x- 8) = 0

6x = 0 , x-8=0

x=0, x =8

1) f^'(x) > 0 , if x<0 and x>8 So, f(x) increases in (-$\infin$, 0) U (7, $\infin$)

2). f^'(x) < 0 , if 0<x<8

So, f(x) decreases in (0,8)