Find the minimum value of f(x)=-x^{2}-x-4 in the interval [-3,3]. The

Madeline Lott

Madeline Lott

Answered question

2021-12-11

Find the minimum value of f(x)=x2x4 in the interval [-3,3].
The absolute minimum value is 154 at x=12
The absolute minimum value is -4 at x=0
The absolute minimum value is -10 at x=-3
The absolute minimum value is -16 at x=3

Answer & Explanation

rodclassique4r

rodclassique4r

Beginner2021-12-12Added 37 answers

Step 1
f(x)=x2x4
f'(x)=-2x-1
To find critical value, put f'(x)=0
0=-2x-1
-2x=1
x=12
x=12
Step 2
x=-3 in f(x)
f(3)=(3)2(3)4
=9+3-4
f(-3)=-10
f(3)=(3)2(3)4
=-9-3-4
=-16
f(12)=(12)2(12)4
=14+124
=1+2164=154
So, absolute minimum value is -16 at x = 3

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