Question

location
Determine the
and values
of absolutely
maximum and
absolutely minimum
for given function
f(x) = (-x+2)^4
where [0,3]​

Answer 1

Answer:

f(x)=2x

3

−15x

2

+36x+1

f

′

(x)=6x

2

−30x+36

Putting f

′

(x)=0

6x

2

−30x+36=0

x

2

−5x+6=0

(x−2)(x−3)=0

x=2 or 3

We are given interval [1,5]

Hence, calculating f(x) at 2, 3, 1, 5,

f(2)=29

f(3)=28

f(1)=24

f(5)=56

Hence, absolute maximum value is 56 at x=5.

Absolute minimum value is 24 at x=1

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