What is the extreme (x-1)^2(x-2)^3 ?

The extreme (x-1)^2(x-2)^3 is Maximum(1,0),Minimum(7/5 ,-108/3125),Saddle(2,0)

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extreme (x-1)^2(x-2)^3

extreme points

(x - 1)^{2} (x - 2)^{3}

Maximum (1, 0), Minimum (\frac{7}{5}, - \frac{108}{3125}), Saddle (2, 0)

Solution steps

f^{'} (x) = (x - 2)^{2} (x - 1) (5 x - 7)

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \frac{7}{5},

Increasing

: \frac{7}{5} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

(x - 1)^{2} (x - 2)^{3} : 0

Maximum (1, 0)

Plug

x = \frac{7}{5}

into

(x - 1)^{2} (x - 2)^{3} : - \frac{108}{3125}

Minimum (\frac{7}{5}, - \frac{108}{3125})

Plug

x = 2

into

(x - 1)^{2} (x - 2)^{3} : 0

Saddle (2, 0)

Maximum (1, 0), Minimum (\frac{7}{5}, - \frac{108}{3125}), Saddle (2, 0)

f (x) = sin (- \frac{2 x}{3})

f (x) = \frac{3 e ^{x}}{e ^{x} - 2}

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

f (x) = \frac{3 x}{x ^{2} - 3}

f (x) = 7 - 5 x

What is the extreme (x-1)^2(x-2)^3 ?
The extreme (x-1)^2(x-2)^3 is Maximum(1,0),Minimum(7/5 ,-108/3125),Saddle(2,0)