Let y = f (x) and y = g (x) be two differentiable function in [0,2] such that f(0) = 3, f

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5. Continuity and Differentiation

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Let $y = f (x)$ and $y = g (x)$ be two differentiable function in $[0,2]$ such that $f(0) = 3,$ $f(2) = 5$ , $g (0) = 1$ and $g(2) = 2$. If there exist atlellst one $c \in \left( {0,2} \right)$ such that $f'(c)=kg'(c)$,then $k$ must be

A

$2$

B

$3$

C

$\frac{1}{2}$

D

$1$

Solution

Let $h(x)=f(x)-k g(x)$ and $h^{\prime}(c)=0$

$\because$ Rolle's theorem is applicable

$\Rightarrow h(0)=h(2)$

$3-\mathrm{k}=5-2 \mathrm{k} \Rightarrow \mathrm{k}=2$

Standard 12

Mathematics

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