Find the critical points of the following functions on the given intervals. Identify the absolute maximum and absolute minimum values (if they exist). f(x)=x^{3}-6x^{2} text{on} [-1,5]

sanuluy

sanuluy

Answered question

2020-11-01

Find the critical points of the following functions on the given intervals. Identify the absolute maximum and absolute minimum values (if they exist). f(x)=x36x2on[1,5]

Answer & Explanation

Dora

Dora

Skilled2020-11-02Added 98 answers

Step 1 Let us find the critical points , absolute maximum and minimum of given function Given: f(x)=x36x2on[1,5]

Step 2 f(x)=x36x2
f(x)=3x212x
0=3x(x4)
3x=0,x4=0
x=0,x=4 Critical point =0,4

Step 3 To find absolute maximum and absolute minimum: f(x)=x36x2
x=1
f(1)=(1)36(1)2
f(1)=16
f(1)=7
x=0
f(0)=06(0)
f(0)=0
x=4
f(4)=436(4)2
f(4)=646(16)
f(4)=6496
f(4)=32
x=5
f(5)=536(5)2
f(5)=125150
f(5)=25 Absolute maximum at y=0, x=0 Absolute minimum at y=-32, x=5

Step 4 Answer: Critical points at x=0,4 Absolute maximum at x=0 Absolute minimum at x=5

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

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?