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

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

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

extreme points

f (x) = (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)

m o n o t o n e x^{4} - 12 x^{3} + 48 x^{2} - 64 x

in v erse f (x) = \frac{6 x - 1}{2 x + 9}

p er p e n d i c u l a r y - 4 = \frac{4}{5} (x - 5) (- 4 - 2)

e x t re m e x - \frac{4}{x ^{2}}

d o main (x + 4)^{2} - 6

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