What is the extreme 8x^6-13x^5 ?

The extreme 8x^6-13x^5 is Saddle(0,0),Minimum(65/48 ,(65^6)/(1528823808)-(65^5*13)/(254803968))

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extreme 8x^6-13x^5

extreme points

8 x^{6} - 13 x^{5}

Saddle (0, 0), Minimum (\frac{65}{48}, \frac{6 5 ^{6}}{1528823808} - \frac{6 5 ^{5} \cdot 13}{254803968})

Solution steps

f^{'} (x) = 48 x^{5} - 65 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{65}{48},

Increasing

: \frac{65}{48} < x < \infty

Plug

x = 0

into

8 x^{6} - 13 x^{5} : 0

Saddle (0, 0)

Plug

x = \frac{65}{48}

into

8 x^{6} - 13 x^{5} : \frac{6 5 ^{6}}{1528823808} - \frac{6 5 ^{5} \cdot 13}{254803968}

Minimum (\frac{65}{48}, \frac{6 5 ^{6}}{1528823808} - \frac{6 5 ^{5} \cdot 13}{254803968})

Saddle (0, 0), Minimum (\frac{65}{48}, \frac{6 5 ^{6}}{1528823808} - \frac{6 5 ^{5} \cdot 13}{254803968})

f (x, y) = x y^{2} - x^{2} y

f (x, y) = y - e - 2 x^{2} y

f (x) = 4 x^{4} + 6 x^{3} - x

f (x) = \frac{x ^{3}}{3} - \frac{5}{2} x^{2} + 4 x + 3

f (x) = 0.502994 x + 2.67066

What is the extreme 8x^6-13x^5 ?
The extreme 8x^6-13x^5 is Saddle(0,0),Minimum(65/48 ,(65^6)/(1528823808)-(65^5*13)/(254803968))