What is the extreme-0.1t^20.8t+98.8,0 = 8 ?

The extreme-0.1t^20.8t+98.8,0 = 8 is Maximum(8,57.84)

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extreme-0.1t^20.8t+98.8,0<= t>= 8

extreme points

- 0.1 t^{2} 0.8 t + 98.8, 0 \leq t \geq 8

Maximum (8, 57.84)

Solution steps

Find the critical points:

t = 8

Domain of

- 0.1 t^{2} 0.8 t + 98.8, 0 \leq t \geq 8 : t \geq 8

Find intervals:

Decreasing

: 8 < t < \infty

Plug the extreme point

x = 8

into

- 0.1 t^{2} 0.8 t + 98.8 \Rightarrow y = 57.84

Maximum (8, 57.84)

f (x) = 4 x^{2} + x y + 252 x + 4 y^{2} - 252 y

f (x) = \frac{t}{1 + t ^{2}}

f (x) = \frac{5}{3} x^{3} - 25 x

f (x) = \frac{x ^{2}}{x - 8}, - 2 \leq x \leq - \frac{1}{4}

f (x) = - 4 x^{4} + 120 x^{2} + 120

What is the extreme-0.1t^20.8t+98.8,0<= t>= 8 ?
The extreme-0.1t^20.8t+98.8,0<= t>= 8 is Maximum(8,57.84)