What is the extreme f(x)=-4/3 x^3-21/2 x^2-5x+14 ?

The extreme f(x)=-4/3 x^3-21/2 x^2-5x+14 is Minimum(-5,-341/6),Maximum(-1/4 , 1403/96)

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extreme f(x)=-4/3 x^3-21/2 x^2-5x+14

extreme points

f (x) = - \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 14

Minimum (- 5, - \frac{341}{6}), Maximum (- \frac{1}{4}, \frac{1403}{96})

Solution steps

f^{'} (x) = - 4 x^{2} - 21 x - 5

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < - \frac{1}{4},

Decreasing

: - \frac{1}{4} < x < \infty

Plug

x = - 5

into

- \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 14 : - \frac{341}{6}

Minimum (- 5, - \frac{341}{6})

Plug

x = - \frac{1}{4}

into

- \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 14 : \frac{1403}{96}

Maximum (- \frac{1}{4}, \frac{1403}{96})

Minimum (- 5, - \frac{341}{6}), Maximum (- \frac{1}{4}, \frac{1403}{96})

f (x, y) = x^{2} + x y + y^{2} - 10 y + 33

f (x) = x^{\frac{1}{5}} (x - 2)

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

f (x) = \frac{( 7 ln ( x ) + 4 )}{x}

f (x) = \frac{24}{x} + 4 π r^{2}

What is the extreme f(x)=-4/3 x^3-21/2 x^2-5x+14 ?
The extreme f(x)=-4/3 x^3-21/2 x^2-5x+14 is Minimum(-5,-341/6),Maximum(-1/4 , 1403/96)