Find the absolute maximum and minimum value. f(x)=-x^{2}+8x+1 on[6,9]

Paligutanhk

Paligutanhk

Answered question

2021-12-07

Find the absolute maximum and minimum value.
f(x)=x2+8x+1 on[6,9]

Answer & Explanation

Charles Benedict

Charles Benedict

Beginner2021-12-08Added 32 answers

Step 1
The function is given by
f(x)=x2+8x+1; [6,9]
To evaluate : The absolute maximum and minimum value
Step 2
Let us first evaluate the critical number
dfdx=0
ddx(x2+8x+1)=0
2x+8=0
x=4 This is a critical number
But the critical number does not lie in the interval [6,9]
Step 3
Now, let us evaluate the values of the function at the endpoints of the given interval.
At x=6,
f(6)=62+8×6+1=13 Absolute maximum value
At x=9,
f(9)=92+8×9+1=8 Absolute minimum value
Hence, the absolute maximum value of the function is 13 and the absolute minimum value of the function is -8

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