What is the extreme f(x)=2x^3-24x^2+72x+7 ?

The extreme f(x)=2x^3-24x^2+72x+7 is Maximum(2,71),Minimum(6,7)

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extreme f(x)=2x^3-24x^2+72x+7

extreme

Maximum (2, 71), Minimum (6, 7)

Solution steps

f^{'} (x) = 6 x^{2} - 48 x + 72

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

2 x^{3} - 24 x^{2} + 72 x + 7 : 71

Maximum (2, 71)

Plug

x = 6

into

2 x^{3} - 24 x^{2} + 72 x + 7 : 7

Minimum (6, 7)

Maximum (2, 71), Minimum (6, 7)

What is the extreme f(x)=2x^3-24x^2+72x+7 ?
The extreme f(x)=2x^3-24x^2+72x+7 is Maximum(2,71),Minimum(6,7)