What is the extreme f(x)=-0.2x^2+1.6x+98.7,0<= x<= 8 ?

The extreme f(x)=-0.2x^2+1.6x+98.7,0<= x<= 8 is Minimum(0,98.7),Maximum(4,101.9),Minimum(8,98.7)

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extreme f(x)=-0.2x^2+1.6x+98.7,0<= x<= 8

extreme points

f (x) = - 0.2 x^{2} + 1.6 x + 98.7, 0 \leq x \leq 8

Minimum (0, 98.7), Maximum (4, 101.9), Minimum (8, 98.7)

Solution steps

Find the critical points:

x = 0, x = 4, x = 8

Domain of

- 0.2 x^{2} + 1.6 x + 98.7, 0 \leq x \leq 8 : 0 \leq x \leq 8

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < 8

Plug the extreme point

x = 0

into

- 0.2 x^{2} + 1.6 x + 98.7 \Rightarrow y = 98.7

Minimum (0, 98.7)

Plug the extreme point

x = 4

into

- 0.2 x^{2} + 1.6 x + 98.7 \Rightarrow y = 101.9

Maximum (4, 101.9)

Plug the extreme point

x = 8

into

- 0.2 x^{2} + 1.6 x + 98.7 \Rightarrow y = 98.7

Minimum (8, 98.7)

Minimum (0, 98.7), Maximum (4, 101.9), Minimum (8, 98.7)

f (x, y) = 3 x^{2} - y^{2}

x^{2} + 4

\frac{x ^{3} + 38 x + 128}{x}, 1 \leq x \leq 10

x^{2} + 9

\frac{1}{x + 6}

What is the extreme f(x)=-0.2x^2+1.6x+98.7,0<= x<= 8 ?
The extreme f(x)=-0.2x^2+1.6x+98.7,0<= x<= 8 is Minimum(0,98.7),Maximum(4,101.9),Minimum(8,98.7)