What is the extreme y=10cos(x)+10sin(x) ?

The extreme y=10cos(x)+10sin(x) is Maximum(pi/4+2pin,10sqrt(2)),Minimum((5pi)/4+2pin,-10sqrt(2))

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extreme y=10cos(x)+10sin(x)

extreme points

y = 10 cos (x) + 10 sin (x)

Maximum (\frac{π}{4} + 2 πn, 102), Minimum (\frac{5 π}{4} + 2 πn, - 102)

Solution steps

Find the critical points:

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

Domain of

10 cos (x) + 10 sin (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

10 cos (x) + 10 sin (x) \Rightarrow y = 102

Maximum (\frac{π}{4} + 2 πn, 102)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

10 cos (x) + 10 sin (x) \Rightarrow y = - 102

Minimum (\frac{5 π}{4} + 2 πn, - 102)

Maximum (\frac{π}{4} + 2 πn, 102), Minimum (\frac{5 π}{4} + 2 πn, - 102)

\frac{( - 6 x + 21 )}{( ( x + 1 ) ^{4} )}

\frac{- 5}{4 x - 8}

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

f (x) = x^{3} + 3 x^{2} - 189 x

f (x) = 1 - ∣ x - 7 ∣

What is the extreme y=10cos(x)+10sin(x) ?
The extreme y=10cos(x)+10sin(x) is Maximum(pi/4+2pin,10sqrt(2)),Minimum((5pi)/4+2pin,-10sqrt(2))