Question:
Mark the correct alternative in the following:
In the interval $(1,2)$, function $f(x)=2|x-1|+3|x-2|$ is
A. increasing
B. decreasing
C. constant
D. none of these
Solution:
Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly decreasing on $(a, b)$ is that $f^{\prime}(x)<0$ for all $x \in(a, b)$
Given:-
$f(x)=2(x-1)+3(2-x)$
$\Rightarrow f(x)=-x+4$
$\frac{d(f(x))}{d x}=f^{\prime}(x)=-1$
Therefore $f^{\prime}(x)<0$
Hence decreasing function
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