What is the extreme b-sin(x) ?

The extreme b-sin(x) is Minimum(pi/2+2pin,b-1),Maximum((3pi)/2+2pin,b+1)

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extreme b-sin(x)

extreme points

b - sin (x)

Minimum (\frac{π}{2} + 2 πn, b - 1), Maximum (\frac{3 π}{2} + 2 πn, b + 1)

Solution steps

Find the critical points:

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

f^{''} (x) = sin (x)

Check the sign of

f^{''} (x) = sin (x)

at each critical point

Check critical point

x = \frac{π}{2} + 2 πn :

Minimum

(\frac{π}{2} + 2 πn, b - 1)

Check critical point

x = \frac{3 π}{2} + 2 πn :

Maximum

(\frac{3 π}{2} + 2 πn, b + 1)

Minimum (\frac{π}{2} + 2 πn, b - 1), Maximum (\frac{3 π}{2} + 2 πn, b + 1)

f (x) = x^{3} + 15 x - 2

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

y = x^{2} - 3 x

y = 9 - 6 x^{2}, - 2 \leq x \leq 3

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

What is the extreme b-sin(x) ?
The extreme b-sin(x) is Minimum(pi/2+2pin,b-1),Maximum((3pi)/2+2pin,b+1)