Find the absolute maximum value and the absolute minimum value, if any, of the function. g(x)=-x^{2}+2x+6

allhvasstH

allhvasstH

Answered question

2021-06-05

Find the absolute maximum value and the absolute minimum value, if any, of the function.
g(x)=x2+2x+6

Answer & Explanation

Khribechy

Khribechy

Skilled2021-06-06Added 100 answers

Step 1
Given
g(x)=x2+2x+6
To find out absolute max or min , let find out derivative g'(x)
g(x)=2x+2
Now set the derivative =0 and solve for x
2x+2=0
2x=2
x=1
Step 2
To check whether x=1 is maximum or minimum we use second derivative test
g(x)=2x+2g(x)=2
second derivative is negative
so f(x) is maximum at x=1
There is no absolute minimum
Now find out absolute maximum value at x=1
Substitute x=1 and find out g(1)
g(1)=12+2(1)+6
g(1)=7
So absolute maximum value is 7
Absolute minimum does not exists

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