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.

Question

Holly Turner

Mathematics

28 February, 17:20

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.

+5

Answers (1)

Know the Answer?

Jacob Stanley · Answer 1

x = - b / (2a)

Step-by-step 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).