Find the absolute max and min values at the indicated interval f(x)=2x^{3}-x^{2}-4x+10, \left[-1,0\right]

Trent Carpenter

Trent Carpenter

Answered question


Find the absolute max and min values at the indicated interval

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-01-26Added 75 answers

Absolute maximum and absolute minimum values of a function exist at a point where its first derivative is zero or at the end points of the given interval.
So first we find the derivative of the given function:
Now fprime(x)=0
x1=0 or 6x+4=0
x=1 or x=23
Now computing the value of the function at these points and at the end points of the interval:
at x=1,f(1)=f(x)=2(1)3(1)24(1)+10=11
at x=0,f(0)=f(x)=2(0)3(0)24(0)+10=10
at x=23,f(23)=f(x)=2(23)3(23)24(23)+10=12.8148
We didn't find the value of f(1), because 1 does not belongs to the interval [-1,0].
Hence absolute maximum value is 12.8148 and absolute minimum value is 10.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-11Added 2605 answers

Answer is given below (on video)

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