What is the extreme f(x)=7sin(x)+7cos(x) ?

The extreme f(x)=7sin(x)+7cos(x) is Maximum(pi/4+2pin,7sqrt(2)),Minimum((5pi)/4+2pin,-7sqrt(2))

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extreme f(x)=7sin(x)+7cos(x)

extreme points

f (x) = 7 sin (x) + 7 cos (x)

Maximum (\frac{π}{4} + 2 πn, 72), Minimum (\frac{5 π}{4} + 2 πn, - 72)

Solution steps

Find the critical points:

x = \frac{π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Domain of

7 sin (x) + 7 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{4} + 2 πn,

Decreasing

: \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn,

Increasing

: \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{4} + 2 πn

into

7 sin (x) + 7 cos (x) \Rightarrow y = 72

Maximum (\frac{π}{4} + 2 πn, 72)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

7 sin (x) + 7 cos (x) \Rightarrow y = - 72

Minimum (\frac{5 π}{4} + 2 πn, - 72)

Maximum (\frac{π}{4} + 2 πn, 72), Minimum (\frac{5 π}{4} + 2 πn, - 72)

f (x) = 5 sin (x) + 5 cos (x), 0 \leq x \leq 2 π

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

f (x) = 242 y^{2} + x^{2} - x^{2} y

f (x, y) = ln (4 - 4 x^{2} - y^{2})

f (x) = \frac{8}{x ^{2} + 2}

What is the extreme f(x)=7sin(x)+7cos(x) ?
The extreme f(x)=7sin(x)+7cos(x) is Maximum(pi/4+2pin,7sqrt(2)),Minimum((5pi)/4+2pin,-7sqrt(2))