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The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.

1 Answer

  • Let $f(x)$ be a function defined on $(a,b)$. If $f'(x)>0$ for all $x \in (a,b)$ except for a finite number of points, where $f'(x)>0,$ then $f(x)$ is increasing on $(a,b)$
Step 1
$f(x)= \sin x-ax+b$
differentiating w.r.t $x$ we get,
$f'(x)= \cos x-a$
when $f'(x)$ is an increasing function
$ f'(x)>0 \Rightarrow \cos x-a >0$
$ \cos x-a>0$
when $x= \pi, \: \cos \pi = - 1$
$ \Rightarrow \geq - 1$
when $ x=0, \: \cos 0=1$
then $ a \geq 1$
Hence the values of $a$ are $-1, 1$
answered Aug 13, 2013 by thanvigandhi_1