What is the extreme f(x)=-(x-1)^2(x-5) ?

The extreme f(x)=-(x-1)^2(x-5) is Minimum(1,0),Maximum(11/3 , 256/27)

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extreme f(x)=-(x-1)^2(x-5)

extreme

Minimum (1, 0), Maximum (\frac{11}{3}, \frac{256}{27})

Solution steps

f^{'} (x) = - 3 x^{2} + 14 x - 11

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < \frac{11}{3},

Decreasing

: \frac{11}{3} < x < \infty

Plug

x = 1

into

- (x - 1)^{2} (x - 5) : 0

Minimum (1, 0)

Plug

x = \frac{11}{3}

into

- (x - 1)^{2} (x - 5) : \frac{256}{27}

Maximum (\frac{11}{3}, \frac{256}{27})

Minimum (1, 0), Maximum (\frac{11}{3}, \frac{256}{27})

What is the extreme f(x)=-(x-1)^2(x-5) ?
The extreme f(x)=-(x-1)^2(x-5) is Minimum(1,0),Maximum(11/3 , 256/27)