MCQ
${d \over {dx}}\{ \cos (\sin {x^2})\} = $
- A$\sin (\sin {x^2}).\cos {x^2}.2x$
- ✓$ - \sin (\sin {x^2}).\cos {x^2}.2x$
- C$ - \sin (\sin {x^2}).{\cos ^2}x.2x$
- DNone of these
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$(i)$ $f (x)$ is bounded on $a \le x \le b.$
$(ii)$ The equation $f (x) = 0$ has at least one solution in $a < x < b.$
$(iii)$ The maximum and minimum values of $f (x)$ on $a \le x \le b$ occur at points where $f ' (c) = 0$.
$(iv)$ There is at least one point $c$ with $a < c < b$ where $f ' (c) > 0$.
$(v)$ There is at least one point $d$ with $a < d < b$ where $f ' (c) < 0.$