To find the critical numbers of the function g(t) = t^5 - t, we first need to find the derivative of the function.

The derivative of t^5 is 5t^4 and the derivative of -t is -1. So, the derivative of the function g(t) = t^5 - t is g'(t) = 5t^4 - 1.

Next, we set the derivative equal to zero and solve for t:

5t^4 - 1 = 0
5t^4 = 1
t^4 = 1/5
t = ±(1/5)^(1/4)

However, we are given that t

Question

To find the critical numbers of the function g(t) = t^5 - t, we first need to find the derivative of the function.

The derivative of t^5 is 5t^4 and the derivative of -t is -1. So, the derivative of the function g(t) = t^5 - t is g'(t) = 5t^4 - 1.

Next, we set the derivative equal to zero and solve for t:

5t^4 - 1 = 0
5t^4 = 1
t^4 = 1/5
t = ±(1/5)^(1/4)

However, we are given that t < 4. So, the only critical number within the given domain is t = -(1/5)^(1/4).

Knowee AI · Accepted Answer

To find the critical numbers of the function g(t) = t^5 - t, we first need to find the derivative of the function.

The derivative of t^5 is 5t^4 and the derivative of -t is -1. So, the derivative of the function g(t) = t^5 - t is g'(t) = 5t^4 - 1.

Next, we set the derivative equal to zero and solve for t:

5t^4 - 1 = 0
5t^4 = 1
t^4 = 1/5
t = ±(1/5)^(1/4)

However, we are given that t < 4. So, the only critical number within the given domain is t = -(1/5)^(1/4).

Find the critical numbers of the function. (Enter your answers as a comma-separated list.)g(t) = t5 − t, t < 4