What is the extreme f(x)=-x^2+10x-21,3<= x<= 7 ?

The extreme f(x)=-x^2+10x-21,3<= x<= 7 is Minimum(3,0),Maximum(5,4),Minimum(7,0)

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extreme f(x)=-x^2+10x-21,3<= x<= 7

extreme points

f (x) = - x^{2} + 10 x - 21, 3 \leq x \leq 7

Minimum (3, 0), Maximum (5, 4), Minimum (7, 0)

Solution steps

Find the critical points:

x = 3, x = 5, x = 7

Domain of

- x^{2} + 10 x - 21, 3 \leq x \leq 7 : 3 \leq x \leq 7

Find intervals:

Increasing

: 3 < x < 5,

Decreasing

: 5 < x < 7

Plug the extreme point

x = 3

into

- x^{2} + 10 x - 21 \Rightarrow y = 0

Minimum (3, 0)

Plug the extreme point

x = 5

into

- x^{2} + 10 x - 21 \Rightarrow y = 4

Maximum (5, 4)

Plug the extreme point

x = 7

into

- x^{2} + 10 x - 21 \Rightarrow y = 0

Minimum (7, 0)

Minimum (3, 0), Maximum (5, 4), Minimum (7, 0)

f (x) = 4 x^{5} - 25 x^{4} - 40 x^{3} - 4

y = x 5 - x

f (x) = 144 - x^{2}

f (x) = \frac{x ^{3} - 4}{x ^{2}}

f (x) = x^{3} + 3 x^{2} - 45 x + 6

What is the extreme f(x)=-x^2+10x-21,3<= x<= 7 ?
The extreme f(x)=-x^2+10x-21,3<= x<= 7 is Minimum(3,0),Maximum(5,4),Minimum(7,0)