What is the extreme 6y=2x^3-27x^2+108x ?

The extreme 6y=2x^3-27x^2+108x is Maximum(3, 45/2),Minimum(6,18)

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extreme 6y=2x^3-27x^2+108x

extreme points

6 y = 2 x^{3} - 27 x^{2} + 108 x

Maximum (3, \frac{45}{2}), Minimum (6, 18)

Solution steps

f^{'} (x) = x^{2} - 9 x + 18

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 3

into

\frac{2 x ^{3} - 27 x ^{2} + 108 x}{6} : \frac{45}{2}

Maximum (3, \frac{45}{2})

Plug

x = 6

into

\frac{2 x ^{3} - 27 x ^{2} + 108 x}{6} : 18

Minimum (6, 18)

Maximum (3, \frac{45}{2}), Minimum (6, 18)

∣ x ∣ + ∣ x + 1 ∣ + x^{2} + 1

y = x z

2 cos^{2} (x)

f (x, y) = 4 x^{2} + y^{2} + 1

f (x) = 5 e^{x^{2} - 10 x}

What is the extreme 6y=2x^3-27x^2+108x ?
The extreme 6y=2x^3-27x^2+108x is Maximum(3, 45/2),Minimum(6,18)