Find the absolute maximum value of g(x)= 2x^{2} −2x−2 over

pogonofor9z

pogonofor9z

Answered question

2021-12-07

Find the absolute maximum value of g(x)=2x22x2 over [0,6].

Answer & Explanation

Daniel Cormack

Daniel Cormack

Beginner2021-12-08Added 34 answers

Step 1
We have to find absolute maximum value of f(x) in given interval.
F(x) is given as:
g(x)=2x22x2, [0,6]
Step 2
We will use following rules of derivative.
Rules are given below:
power rule : ddx[xn]=nxn1
Step 3
With the help of above rules we will find f'(x) and then put equals to zero to find critical points.
After that we will find value of f(x) at boundaries of given interval and at critical points (lies in given interval).
Maximum value of f(x) at these points will give absolute maximum value.
Work is shown below:
g(x)=2x22x2, [0,6]
g(x)=4x2
g(x)=0
4x2=0
x=12
g(0)=2
g(12)=2(12)212=52
g(6)=2(6)2122=58
absolute maximum is 58 at x=6
Step 4
Answer
absolute maximum is 58 at x=6

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