What is the extreme f(x)=t^3-15t^2+72t+8 ?

The extreme f(x)=t^3-15t^2+72t+8 is Maximum(4,120),Minimum(6,116)

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extreme f(x)=t^3-15t^2+72t+8

extreme points

f (x) = t^{3} - 15 t^{2} + 72 t + 8

Maximum (4, 120), Minimum (6, 116)

Solution steps

f^{'} (t) = 3 t^{2} - 30 t + 72

Find intervals:

Increasing

: - \infty < t < 4,

Decreasing

: 4 < t < 6,

Increasing

: 6 < t < \infty

Plug

t = 4

into

t^{3} - 15 t^{2} + 72 t + 8 : 120

Maximum (4, 120)

Plug

t = 6

into

t^{3} - 15 t^{2} + 72 t + 8 : 116

Minimum (6, 116)

Maximum (4, 120), Minimum (6, 116)

f (x) = \frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9

R (x, y) = - 5 x^{2} - 4 y^{2} - 4 x y + 68 x + 72 y

f (x, y) = 9 - x^{2} - 2 y^{2}

y = x^{2} - 6 x + 5

\frac{d}{d t} (- 4.9 t^{2} + x + 21)

What is the extreme f(x)=t^3-15t^2+72t+8 ?
The extreme f(x)=t^3-15t^2+72t+8 is Maximum(4,120),Minimum(6,116)