What is the critical h(x)=sin^2(x)+cos(x) ?

The critical h(x)=sin^2(x)+cos(x) is x=2pin,x= pi/3+2pin,x=pi+2pin,x=(5pi)/3+2pin

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critical h(x)=sin^2(x)+cos(x)

critical points

h (x) = sin^{2} (x) + cos (x)

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

Solution steps

sin^{2} (x) + cos (x)

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

sin^{2} (x) + cos (x) : - \infty < x < \infty

All critical points are in domain

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

f (x) = 5 x^{2} + 1

\frac{1 - 5 t}{3 + t}

f (x) = - 3 x - 1

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

(- 1, - 5), (5, - 3)

What is the critical h(x)=sin^2(x)+cos(x) ?
The critical h(x)=sin^2(x)+cos(x) is x=2pin,x= pi/3+2pin,x=pi+2pin,x=(5pi)/3+2pin