Analyzing Functions

Question

Find the critical point of the function f(x) = -x² + 4x - 5.

Options:

1. (2 , -1)
2. (2 , 0)
3. (-2 , -37)
4. (2 , 1)

Answer 1

Critical points occur where f'(x) = 0 or f'(x) does not exist. Since f(x) in your problem is a polynomial function, it is differentiable everywhere and the only critical point it may have is when f'(x) = 0.

Find f'(x)

f'(x) = -2x + 4

Determine when f'(x) = 0

f'(x) = -2x + 4 = 0

-2x = -4

x = 2

Find the y-value of the critical point

f(2) = -(2)² + 4(2) - 5 = -4 + 8 - 5 = -1

Critical Point (2, -1)