What is the extreme f(x)=-3/5 x^5+9x^4-35x^3+6 ?

The extreme f(x)=-3/5 x^5+9x^4-35x^3+6 is Saddle(0,6),Minimum(5,-619),Maximum(7,-2371/5)

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extreme f(x)=-3/5 x^5+9x^4-35x^3+6

extreme points

f (x) = - \frac{3}{5} x^{5} + 9 x^{4} - 35 x^{3} + 6

Saddle (0, 6), Minimum (5, - 619), Maximum (7, - \frac{2371}{5})

Solution steps

f^{'} (x) = - 3 x^{4} + 36 x^{3} - 105 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 0

into

- \frac{3}{5} x^{5} + 9 x^{4} - 35 x^{3} + 6 : 6

Saddle (0, 6)

Plug

x = 5

into

- \frac{3}{5} x^{5} + 9 x^{4} - 35 x^{3} + 6 : - 619

Minimum (5, - 619)

Plug

x = 7

into

- \frac{3}{5} x^{5} + 9 x^{4} - 35 x^{3} + 6 : - \frac{2371}{5}

Maximum (7, - \frac{2371}{5})

Saddle (0, 6), Minimum (5, - 619), Maximum (7, - \frac{2371}{5})

f (x) = x - y

f (x, y) = x - y

f (x, y) = y^{4} + x^{2} - 8 y^{2} + 2 x

f (x) = 2 x^{3} + 3 x^{2} + 4

f (x) = x^{3} + 3 y^{3} + 3 x^{2} + 3 y^{2} + 24

What is the extreme f(x)=-3/5 x^5+9x^4-35x^3+6 ?
The extreme f(x)=-3/5 x^5+9x^4-35x^3+6 is Saddle(0,6),Minimum(5,-619),Maximum(7,-2371/5)