Question

Consider the following. (If an answer does not exist, enter DNE.) [ f(x)=x⁶ e^-x ] (a) Find the interval(s) on which ( f ) is increasing. (Enter your answer using interval notation.) (b) Find

Answer 1

To determine the interval of increase for the function f(x)=x^6e^{-x}, we need to find where the derivative of the function is positive.

Step-by-step explanation:

(a) To find the interval(s) on which the function is increasing, we need to find where the derivative of the function is positive. The derivative of f(x) is:

f'(x) = 6x^5e^{-x} - x^6e^{-x}

To find the interval(s) where f'(x) > 0, we can set the derivative equal to 0:

6x^5e^{-x} - x^6e^{-x} = 0

Unfortunately, finding the exact values for x where this equation equals 0 is quite complicated and cannot be expressed in simple terms. Therefore, we can't find the exact interval(s) where f(x) is increasing, but we can determine some properties about the function.

(b) The question cuts off after part (b). Please provide the complete question so I can help you further.

Learn more about Increasing interval