Find the absolute extrema if they exist, and all values

kuvitia9f

kuvitia9f

Answered question

2021-12-14

Find the absolute extrema if they exist, and all values of x where they occur on the given intervals.
f(x)=x3+2x215x+3;[4,2]

Answer & Explanation

deginasiba

deginasiba

Beginner2021-12-15Added 31 answers

Step 1
Let f(x)=x3+2x215x+3
The given interval is [-4,2]
To find absolute extrema we have to deduct absolute maximum and absolute minimum
Step 2
First we have to find the critical numbers of f(x) in (-4,2). For finding critical numbers we have to solve the first derivative of f(x).
f(x)=x3+2x215x+3
f(x)=3x2+415
So equating f'(x)=0
3x2+4x15=0
The values of x= -3 , 5/3
The absolute extrema occurs.
Step 3
Then we have to find the values of f(x) at the critical points and intervals.
f(-3)=39
f(5/3)=-11.815
f(-4)=31
f(2)=-11
Step 4
The absolute maximum value will be 39 at x=-3
The absolute minimum value will be -11.815 at x=5/3

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