What is the extreme f(x)=x^6-3x^5 ?

The extreme f(x)=x^6-3x^5 is Saddle(0,0),Minimum(5/2 ,-3125/64)

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extreme f(x)=x^6-3x^5

extreme points

f (x) = x^{6} - 3 x^{5}

Saddle (0, 0), Minimum (\frac{5}{2}, - \frac{3125}{64})

Solution steps

f^{'} (x) = 6 x^{5} - 15 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

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

Increasing

: \frac{5}{2} < x < \infty

Plug

x = 0

into

x^{6} - 3 x^{5} : 0

Saddle (0, 0)

Plug

x = \frac{5}{2}

into

x^{6} - 3 x^{5} : - \frac{3125}{64}

Minimum (\frac{5}{2}, - \frac{3125}{64})

Saddle (0, 0), Minimum (\frac{5}{2}, - \frac{3125}{64})

f (x) = x^{2} - 3 x + 1

(5, 5), (- 10, - 2)

f (x) = 1 - x^{2}

y = x^{2} + 1

f (x) = x^{2} tan (x)

What is the extreme f(x)=x^6-3x^5 ?
The extreme f(x)=x^6-3x^5 is Saddle(0,0),Minimum(5/2 ,-3125/64)