What is the extreme f(x)=-(15x^4)/4-(5x^3)/3-4 ?

The extreme f(x)=-(15x^4)/4-(5x^3)/3-4 is Maximum(-1/3 ,-1291/324),Saddle(0,-4)

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extreme f(x)=-(15x^4)/4-(5x^3)/3-4

extreme points

f (x) = - \frac{15 x ^{4}}{4} - \frac{5 x ^{3}}{3} - 4

Maximum (- \frac{1}{3}, - \frac{1291}{324}), Saddle (0, - 4)

Solution steps

f^{'} (x) = - 15 x^{3} - 5 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{1}{3}

into

- \frac{15 x ^{4}}{4} - \frac{5 x ^{3}}{3} - 4 : - \frac{1291}{324}

Maximum (- \frac{1}{3}, - \frac{1291}{324})

Plug

x = 0

into

- \frac{15 x ^{4}}{4} - \frac{5 x ^{3}}{3} - 4 : - 4

Saddle (0, - 4)

Maximum (- \frac{1}{3}, - \frac{1291}{324}), Saddle (0, - 4)

f (x) = \frac{( x ^{2} - 11 x + 82 )}{x - 9}

p (x) = x^{2} (a + 3) x^{3} + 2 x + a^{2} + 5

R (x, y) = x^{2} + 5 x y + 6 y^{2} + 7 x + 17 y + 12

f (x) = - 10 x^{2} + 1660 x - 49000

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

What is the extreme f(x)=-(15x^4)/4-(5x^3)/3-4 ?
The extreme f(x)=-(15x^4)/4-(5x^3)/3-4 is Maximum(-1/3 ,-1291/324),Saddle(0,-4)