Mark the correct alternative in the following:

Question:

Mark the correct alternative in the following:

In the interval $(1,2)$, function $f(x)=2|x-1|+3|x-2|$ is

A. monotonically increasing

B. monotonically decreasing

C. not monotonic

D. constant

Solution:

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly decreading on $(a, b)$ is that $f^{\prime}(x)<0$ for all $x \in(a, b)$

Given:-

$f(x)=2(x-1)+3(2-x)$

$f(x)=-x+4$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=-1=\mathrm{f}(\mathrm{x})$

Therefore $f^{\prime}(x)<0$

Hence decreasing function

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