Given g(x)=-2x^{2}+x-1, find the absolute maximum value over the interval

Rena Giron

Rena Giron

Answered question

2021-12-06

Given g(x)=2x2+x1, find the absolute maximum value over the interval [−2,4].

Answer & Explanation

Cherry McCormick

Cherry McCormick

Beginner2021-12-07Added 23 answers

 We have:
g(x)=2x2+x1
So, g(x)=d dx (2x2+x1)
=-4x+1
For critical points, g'(x)=0
Or, -4x+1=0
Or, x=14
Then, g (x)=d dx (4x+1)=4<0
So, g(x) will be maximum at 14
So, the critical points are 14,2,4
Now, check the value at each critical point:
g(2)=2(2)2+(2)1=11
g(14)=2(14)2+(14)1=78=0.875
g(4)=2(4)2+41=29
So, absolute value of g(x) will occur at x=14 and the absolute maximum value is 78=0.875

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