lubna6792

lubna6792

Answered question

2022-04-03

Answer & Explanation

star233

star233

Skilled2022-04-20Added 403 answers

f(x)=x2-3x23 , [0,2]

Find the critical points.

Find the first derivative.

2x-2x13

Set the first derivative equal to 00 then solve the equation 2x-2x13=0.

x=1,-1

Find the values where the derivative is undefined.

x=0

Evaluate x2-3x23 at each x value where the derivative is 0 or undefined.

(1,-2),(-1,-2),(0,0)

Exclude the points that are not on the interval.

(1,-2),(0,0)

Evaluate at the included endpoints.

(0,0),(2,4-3223)

Compare the f(x) values found for each value of x in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest f(x) value and the minimum will occur at the lowest f(x) value.

Absolute Maximum: (0,0)

Absolute Minimum:  (1,-2)

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