Find the maximum value of f(x)=2x^{2}+5x-1 in the given interval

Mary Jackson

Mary Jackson

Answered question

2021-12-10

Find the maximum value of f(x)=2x2+5x1 in the given interval [0,3].
The absolute maximum value is -1 at x=0.
The absolute maximum value is 32 at x=3
The absolute maximum value is 338 at x=54
The absolute maximum value is 14 at x=32

Answer & Explanation

Jordan Mitchell

Jordan Mitchell

Beginner2021-12-11Added 31 answers

Given,
f(x)=2x2+5x1
Differentiating with respect to x, we get
f'(x)=2(2x)+5(1)-0
f(x)=4x+5
Now to find critical values, solve the first derivative by equating it to zero. That is,
f'(x)=0
4x+5=0
4x=5
x=54
Step 2
But 54 not [0,3].
Therefore find the value of the function at the end points of the given interval.
When x=0,
f(0)=2(0)2+5(0)1
=-1
When x=3,
f(3)=2(3)2+5(3)1
=32
Hence absolute maximum value is 32 at x=3.

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