Question

Consider the function f(x) = -4x^2 + 4x - 7. Find the critical value(s), x_0, of the function.

a) x_0 = 1
b) x_0 = 2
c) x_0 = -1
d) x_0 = 0

Answer 1

The critical value of the function f(x) = -4x^2 + 4x - 7 is x_0 = 1/2.

Step-by-step explanation:

The critical values of a function occur at the points where the derivative of the function is equal to zero. To find the critical values of the function f(x) = -4x^2 + 4x - 7, we need to find the values of x that satisfy the equation f'(x) = 0.

First, let's find the derivative of the function: f'(x) = -8x + 4.

Setting f'(x) = 0, we have -8x + 4 = 0. Solving this equation gives us x = 1/2. Therefore, the critical value of the function is x_0 = 1/2.