What is the extreme f(x)=cos(x)-5x,0<= x<= 4pi ?

The extreme f(x)=cos(x)-5x,0<= x<= 4pi is Maximum(0,1),Minimum(4pi,1-20pi)

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extreme f(x)=cos(x)-5x,0<= x<= 4pi

extreme points

f (x) = cos (x) - 5 x, 0 \leq x \leq 4 π

Maximum (0, 1), Minimum (4 π, 1 - 20 π)

Solution steps

Find the critical points:

x = 0, x = 4 π

Domain of

cos (x) - 5 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) - 5 x \Rightarrow y = 1

Maximum (0, 1)

Plug the extreme point

x = 4 π

into

cos (x) - 5 x \Rightarrow y = 1 - 20 π

Minimum (4 π, 1 - 20 π)

Maximum (0, 1), Minimum (4 π, 1 - 20 π)

4 x^{3} - 6 x

y \cdot ln (x) + y

5 x + 5 sin (x)

80 x - 16 x^{2}

f (x) = 19 + 4 x - x^{2}, 0 \leq x \leq 5

What is the extreme f(x)=cos(x)-5x,0<= x<= 4pi ?
The extreme f(x)=cos(x)-5x,0<= x<= 4pi is Maximum(0,1),Minimum(4pi,1-20pi)