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Popular >

extreme f(x)=4x-8sin(x)

Solution

extreme points

f (x) = 4 x - 8 sin (x)

Solution

Minimum (\frac{π}{3} + 2 πn, 4 (\frac{π}{3} + 2 πn) - 8 sin (\frac{π}{3} + 2 πn)), Maximum (\frac{5 π}{3} + 2 πn, 4 (\frac{5 π}{3} + 2 πn) - 8 sin (\frac{5 π}{3} + 2 πn))

Solution steps

Find the critical points:

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Domain of

4 x - 8 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{3} + 2 πn,

Increasing

: \frac{π}{3} + 2 πn < x < \frac{5 π}{3} + 2 πn,

Decreasing

: \frac{5 π}{3} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{3} + 2 πn

into

4 x - 8 sin (x) \Rightarrow y = 4 (\frac{π}{3} + 2 πn) - 8 sin (\frac{π}{3} + 2 πn)

Minimum (\frac{π}{3} + 2 πn, 4 (\frac{π}{3} + 2 πn) - 8 sin (\frac{π}{3} + 2 πn))

Plug the extreme point

x = \frac{5 π}{3} + 2 πn

into

4 x - 8 sin (x) \Rightarrow y = 4 (\frac{5 π}{3} + 2 πn) - 8 sin (\frac{5 π}{3} + 2 πn)

Maximum (\frac{5 π}{3} + 2 πn, 4 (\frac{5 π}{3} + 2 πn) - 8 sin (\frac{5 π}{3} + 2 πn))

Minimum (\frac{π}{3} + 2 πn, 4 (\frac{π}{3} + 2 πn) - 8 sin (\frac{π}{3} + 2 πn)), Maximum (\frac{5 π}{3} + 2 πn, 4 (\frac{5 π}{3} + 2 πn) - 8 sin (\frac{5 π}{3} + 2 πn))

Popular Examples

domain of f(x)=((x^2-4))/((x-2))domain

f (x) = \frac{( x ^{2} - 4 )}{( x - 2 )}

domain of f(x)= 2/(x^2+2x)domain

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

inflection (x^2-2x-3)/x inflection points

\frac{x ^{2} - 2 x - 3}{x}

inverse of f(x)= 1/4 x+7 inverse

f (x) = \frac{1}{4} x + 7

inverse of f(x)=0.6x^2-1.5x+1 inverse

f (x) = 0.6 x^{2} - 1.5 x + 1

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x-8sin(x) ?
The extreme f(x)=4x-8sin(x) is