Find the absolute extrema of the function on the closed

Irrerbthist6n

Irrerbthist6n

Answered question

2021-12-09

Find the absolute extrema of the function on the closed interval.
f(x)=x2+5x,[4,0]

Answer & Explanation

einfachmoipf

einfachmoipf

Beginner2021-12-10Added 32 answers

Given,
f(x)=x2+5x,[4,0]
Absolute extrema of the function on the closed interval occurs at a point where its first derivative is zero or at the end points of the given interval.
So differentiating f(x) with respect to x, we get
f'(x)=2x+5
Now f'(x)=0
2x+5=0
2x=5
x=2.5
Step 2
Now,
f(4)=(4)2+5(4)=1620=4
f(2.5)=(2.5)2+5(2.5)=6.2512.5=6.25
f(0)=(0)2+5(0)=0+0=0
Hence absolute maximum value is 0 occurs at the point x = 0 and absolute minimum value is -6.25 occurs at the point
x = -2.5

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