The extreme values of a function occur at the points where the derivative is equal to 0.

f(x) = 2x^3 + 3x^2 - 12x + 5

=> f'(x) = 6x^2 + 6x - 12

6x^2 + 6x - 12 = 0

=> x^2 + x - 2 = 0

=> x^2 + 2x - x - 2 = 0

=> x(x + 2) - 1(x + 2) = 0

=> (x - 1)(x + 2) = 0

x = 1 and x = -2

f(x) = -2 for x = 1 and f(x) = 25 for x = -2.

**The extreme values are x1 = -2 and x2 = 25.**

Posted on

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now