Determine where the absolute extrema of f(x)=-5x^{2}+14x on the interval

smellmovinglz

smellmovinglz

Answered question

2021-12-06

Determine where the absolute extrema of f(x)=5x2+14x on the interval [1,3] occur.
The absolute maximum occurs at x= B
The absolute minimum occurs at x= B

Answer & Explanation

Hiroko Cabezas

Hiroko Cabezas

Beginner2021-12-07Added 18 answers

Step 1
Given function is
f(x)=5x2+14x
Step 2
Firstly, we find stationary points of f(x) by solving f'(x)=0
f'(x)=-10x+14
f'(x)=0
-10x+14=0
x=75
Step 3
Now, we find f(1), f(7/5) and f(3)
f(x)=5x2+14x
f(1)=5(1)2+14(1)=9
f(75)=5(75)2+14(75)=495
f(3)=5(3)2+14(3)=3
Step 4
Ans: absolute maximum value occur at x=1 andsolute minimum value occur at x=3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?