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Question

Find the maximum and minimum value of function f(x)=x3−6x2+9x+1 in the interval x=0 to x=5.

A
21 and 1
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B
20 and 2
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C
16 and 14
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D
18 and 2
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Solution

The correct option is A 21 and 1
First, isolate the possible values of x at which maximum and minimum value of function possible which is x=0 and x=5.

Now find out the critical points by using
f(x)=0
f(x)=3x212x+9=0
3(x1)(x3)=0
x=1,3

So to find out the maximum and minimum value, just calculate the value of function at x=0,1,3,5 and compare.
x0135f(x)15121

Hence, maximum value is 21 and minimum value is 1.

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