Find the absolute extrema on the given interval. f(x)=x^{3}-6x^{2}+5,\ [-3,5]

Susan Munoz

Susan Munoz

Answered question

2021-12-05

Find the absolute extrema on the given interval.
f(x)=x36x2+5, [3,5]

Answer & Explanation

Stephanie Mann

Stephanie Mann

Beginner2021-12-06Added 25 answers

Step 1
To find the absolute extrema on the given interval.
Given function is f(x)=x36x2+5 and interval is [-3,5].
First, we must identify the function's crucial points.
Separating the provided function from x.
f(x)=d dx (x36x2+5)
=3x212x+0
=3x212x
Putting first derivative equals to zero.
3x212x=0
3x(x-4)=0
x(x-4)=0
x=0 or (x-4)=0
x=0 or x=4
Step 2
Critical values are 0 and 4.
Both 0 and 4 lies in the interval [-3,5].
Endpoints of interval are -3 and 5.
Now we will evaluate the value of function at endpoints of the interval and at critical values.
f(3)=(3)36(3)2+5
=-27-54+5
=-81+5
=-76
f(0)=036(0)2+5
=0-0+5
=5
Step 3
f(4)=(4)36(4)2+5
=64-96+5
=69-96
=-27
f(5)=(5)36(5)2+5
=125-150+5
=130-150
=-20
The absolute maximum value of the function is 5 at x=0.
The absolute minimum value of the function is -76 at x=-3.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?