What is the extreme x^3-4x^2-16x+9 ?

The extreme x^3-4x^2-16x+9 is Maximum(-4/3 , 563/27),Minimum(4,-55)

extreme x^3-4x^2-16x+9

extreme points

x^{3} - 4 x^{2} - 16 x + 9

Maximum (- \frac{4}{3}, \frac{563}{27}), Minimum (4, - 55)

Solution steps

f^{'} (x) = 3 x^{2} - 8 x - 16

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - \frac{4}{3}

into

x^{3} - 4 x^{2} - 16 x + 9 : \frac{563}{27}

Maximum (- \frac{4}{3}, \frac{563}{27})

Plug

x = 4

into

x^{3} - 4 x^{2} - 16 x + 9 : - 55

Minimum (4, - 55)

Maximum (- \frac{4}{3}, \frac{563}{27}), Minimum (4, - 55)

in t erce pt s f (x) = 2 (x - 1)^{2} - 8

d o main (x + 2) e^{\frac{1}{x}}

a sy m pt o t es f (x) = \frac{x ^{2} + x}{- x ^{2} + 4 x}

d o main y = arctan (\frac{x - 1}{x + 1})

a sy m pt o t es f (x) = \frac{x ^{3} \cdot e ^{2}}{x \cdot ln ( x ) \cdot e}

What is the extreme x^3-4x^2-16x+9 ?
The extreme x^3-4x^2-16x+9 is Maximum(-4/3 , 563/27),Minimum(4,-55)