Question

Find the critical points in the domain of the function f(x)=4x³ −3x. Enter the exact answers in increasing order. If the number of critical points is less than the number of response areas, enter NA in the remaining response areas.

Answer 1

The critical points of the function f(x) are found by deriving f(x) to get f'(x) = 12x² - 3, setting it equal to zero, and solving for x to obtain x = -1/2 and x = 1/2.

Step-by-step explanation:

To find the critical points of the function f(x) = 4x³ −3x, we must first find the derivative of the function and then set it equal to zero to solve for x. The derivative of f(x) is f'(x) = 12x² - 3. Setting this equal to zero gives:

• 12x² - 3 = 0

Next, we solve for x:

• x² = 3/12
• x² = 1/4
• x = ±1/2

Thus, the critical points of f(x) are at x = -1/2 and x = 1/2. There is no need to enter NA in the remaining response areas because we have two critical points.