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

The extreme f(x)=5x^6-5x^5 is Saddle(0,0),Minimum(5/6 ,-15625/46656)

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

extreme points

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

Saddle (0, 0), Minimum (\frac{5}{6}, - \frac{15625}{46656})

Solution steps

f^{'} (x) = 30 x^{5} - 25 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{5}{6},

Increasing

: \frac{5}{6} < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{5}{6}

into

5 x^{6} - 5 x^{5} : - \frac{15625}{46656}

Minimum (\frac{5}{6}, - \frac{15625}{46656})

Saddle (0, 0), Minimum (\frac{5}{6}, - \frac{15625}{46656})

f (x) = 2 sin (7 x)

f (x) = \frac{7 x}{x ^{2} - 16}

f (x) = \frac{7}{x - 4}

f (x) = 2 x - 78

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

What is the extreme f(x)=5x^6-5x^5 ?
The extreme f(x)=5x^6-5x^5 is Saddle(0,0),Minimum(5/6 ,-15625/46656)