Question

Find all critical numbers of the function: f(x) = 4/x²⁵x

a) x = -4
b) x = 0
c) x = 4
d) x = ±2

Answer 1

To find the critical numbers of the function f(x) = 4/x²⁵x, we need to find the values of x where the derivative of the function is equal to zero or undefined.

Step-by-step explanation:

To find the critical numbers of the function f(x) = 4/x²⁵x, we need to find the values of x where the derivative of the function is equal to zero or undefined.

1. First, find the derivative of the function by applying the power rule and the quotient rule.
2. Set the derivative equal to zero and solve for x. The values of x obtained are the critical numbers.
3. Check for any values where the denominator of the function is equal to zero. These values would make the function undefined.

By following these steps, we can determine the critical numbers of the function and whether any values make the function undefined.