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Popular >

extreme 32ln(x)-x^2

Solution

extreme points

32 ln (x) - x^{2}

Solution

Maximum (4, 64 ln (2) - 16)

Solution steps

f^{'} (x) = \frac{32}{x} - 2 x

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 4

into

32 ln (x) - x^{2} : 64 ln (2) - 16

Maximum (4, 64 ln (2) - 16)

Graph

Popular Examples

extreme f(x)=x^3-2x^2-4x+1 extreme points

f (x) = x^{3} - 2 x^{2} - 4 x + 1

extreme f(x,y)=3x^2+2y^2-6x-4y+16 extreme points

f (x, y) = 3 x^{2} + 2 y^{2} - 6 x - 4 y + 16

extreme f(x)=2x^5-4x^2+5x-3 extreme points

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

extreme 2^x extreme points

2^{x}

extreme y=(4-x)4^x extreme points

y = (4 - x) 4^{x}

Frequently Asked Questions (FAQ)

What is the extreme 32ln(x)-x^2 ?
The extreme 32ln(x)-x^2 is Maximum(4,64ln(2)-16)