Question

Find the critical numbers of g(x) = x¹/7 - x⁻6/7.

a) x = 1, -1
b) x = 0, 1
c) x = 0, -1
d) x = 1, 2

Answer 1

The critical numbers of g(x) are x = 1 and x = -1. Hence, option A is correct.

Step-by-step explanation:

To find the critical numbers of g(x) = x^(1/7) - x^(-6/7), we need to find the values of x where the derivative of g(x) is equal to zero or undefined. The derivative of g(x) can be found using the power rule of differentiation.

The derivative of g(x) is g'(x) = (1/7) * x^(-6/7) + (6/7) * x^(-13/7).

To find the critical numbers, we set g'(x) equal to zero and solve for x: (1/7) * x^(-6/7) + (6/7) * x^(-13/7) = 0.

The critical numbers of g(x) are x = 1 and x = -1.