Question

Find all critical numbers for the given function x√x + 5.

a) x = 0
b) x = -5
c) x = 5
d) x = ±5

Answer 1

To find the critical numbers of the given function x√x + 5, we need to find the values of x where the derivative of the function is equal to zero or undefined. The critical number for the function is x = 1/16.

Step-by-step explanation:

To find the critical numbers of the given function x√x + 5, we need to find the values of x where the derivative of the function is equal to zero or undefined. To find the derivative, we can use the power rule: differentiate x√x and the constant 5, then set it equal to zero:

• 2√x + (1/2)x(-1/2) = 0
• √x + (1/4)√(1/x) = 0
• √x - (1/4)√(1/x) = 0
• √x = (1/4)√(1/x)
• x = (1/16)

So, the critical number for the function is x = 1/16.