Question

Determine the critical values of f(x) = ax² + bx + c.

A critical value can occur where f'(x) = 0 and also where f'(x) does not exist. Since f'(x) is a​ polynomial, there are no​ x-values where f '(x) does not exist.​ Therefore, the only critical values will be where f'(x) = 0.
Solve the equation f'(x) = 0 for x.

Answer 1

x = -b/(2a)

Explanation:

Using the power rule for derivatives, you can find ...

f'(x) = 2ax +b

Solving for x when f'(x) = 0, we have ...

2ax +b = 0

2ax = -b

x = -b/(2a)

The critical value is x = -b/(2a).