The function f(x)=x+sinx has

Options

A. a minimum but no maximum
B. a maximu but no minimum
C. neither maximum nor minimum
D. both maximum and minimum

Answer

C

Explanation

Given, `f(x)=x+sinx`
`thereforef'(x)=1+cosx`
Put f'(x)=0 for maxima or minima.
`implies1+cosx=0`
`impliescosx=cospiimpliesx=pi`
Now, `f"(x)=-sinx`
`f"(pi)=0`
and `f"'(x)=-cosx`
`impliesf"'(pi)=-cospi=1ne0`
Hence, f(x) is neither maximum nor minimum.