Math

QuestionFind the values of xx where f(x)=8x+5f(x)=8x+5 has a local maximum. Options: A. x=x= (integers), B. No local maximum.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=8x+5f(x) =8x +5 . We are looking for the local maximum of the function

STEP 2

A local maximum of a function is a point where the function changes from increasing to decreasing. This occurs where the derivative of the function is zero.

STEP 3

First, we need to find the derivative of the function. The derivative of a linear function like f(x)=8x+5f(x) =8x +5 is a constant.
f(x)=8f'(x) =8

STEP 4

The derivative of the function is a constant, which means the function is always increasing or always decreasing. In this case, since the derivative is positive, the function is always increasing.

STEP 5

Since the function is always increasing, it does not have any points where it changes from increasing to decreasing. Therefore, the function does not have any local maxima.
The correct choice is B. There are no values of xx at which ff has a local maximum.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord