What is the extreme f(x)=cos(x)-2x,0<= x<= 4pi ?

The extreme f(x)=cos(x)-2x,0<= x<= 4pi is Maximum(0,1),Minimum(4pi,1-8pi)

Popular >

extreme f(x)=cos(x)-2x,0<= x<= 4pi

extreme points

f (x) = cos (x) - 2 x, 0 \leq x \leq 4 π

Maximum (0, 1), Minimum (4 π, 1 - 8 π)

Solution steps

Find the critical points:

x = 0, x = 4 π

Domain of

cos (x) - 2 x, 0 \leq x \leq 4 π : 0 \leq x \leq 4 π

Find intervals:

Decreasing

: 0 < x < 4 π

Plug the extreme point

x = 0

into

cos (x) - 2 x \Rightarrow y = 1

Maximum (0, 1)

Plug the extreme point

x = 4 π

into

cos (x) - 2 x \Rightarrow y = 1 - 8 π

Minimum (4 π, 1 - 8 π)

Maximum (0, 1), Minimum (4 π, 1 - 8 π)

f (x) = \frac{7 ( x - 1 ) ^{2}}{x + 9}

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}

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

\frac{d}{d x} ((x + y) 2 + 2 y^{2})

f (x) = \frac{2 ( x + 7 ) ^{2}}{x + 10}

What is the extreme f(x)=cos(x)-2x,0<= x<= 4pi ?
The extreme f(x)=cos(x)-2x,0<= x<= 4pi is Maximum(0,1),Minimum(4pi,1-8pi)