Consider the function f(x)=x^{4}-18x^{2}+1, -2\le x\le 7. Find the absolute minimum

Helen Lewis

Helen Lewis

Answered question

2021-12-09

Consider the function f(x)=x418x2+1,2x7.
Find the absolute minimum value of this function.
Answer: B
find the absolute maximum value of this function.
Answer: B

Answer & Explanation

Andrew Reyes

Andrew Reyes

Beginner2021-12-10Added 24 answers

Step 1
f(x)=x418x2+1   2x7
f(x)=4x336x
Put f(x)=04x336x=0
x(4x236)=0
x=0 and x2=364=9
x=±3
Critical points are 0, +3, -3 2x7
x=0,+3
Step 2
f(2)=(2)418(2)2+1=55
f(0)=0-0+1=1
f(3)=(3)418(3)2+1=80
f(7)=(7)418(7)2+1=1520
Step 3
Absolute maximum (7, 1520)
and Absolute minimum (3, -80)

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?