# The maximum and the minimum values, if any of the following functions
f (x) = sin 3x + 4,

### Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

We have,

*f*(

*x*) = sin 3

*x +*4 for all

_{}

Now,

_{}for all_{}_{}

_{}for all

_{}

_{}

_{}for all

_{}

_{}

_{}for all

_{}

Thus, the maximum value of

*f*(*x*) is 5 and the minimum value is 3.Now,

*f*(*x*) = 5_{}sin 3

*x*

*+*4 = 5

_{}sin 3

*x*= 1

_{}3

*x*=

_{}

_{}

*x*=

_{}

So,

*f*(*x*) attains its maximum values 5 at_{}Also,

*f*(*x*) = 3_{}sin 3*x*+ 4 = 3_{}sin 3*x*= –1_{}3

*x*=

_{}

_{}

*x*=

_{}

So,

*f*(*x*) attains the minimum value 3 at*x*=

_{}

### Answered by | 4th Jun, 2014, 03:23: PM

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