#### Need solution for RD Sharma maths class 12 chapter 17 Maxima and Minima exercise 17 point 1  question 7

Maximum value is 3 and minimum value does not exist.

Hint:

f(x) have max value in [a, b] such that f(x) ≤ f(c) for all x belongs to [a ,b] and if f(x) ≥ f(c) then f(x) has minimum value.

Given:

$f(x)=-|x+1|+3 \text { on } R$

Explanation:

We have,

$f(x)=-|x+1|+3 \text { on } R$

We have,

\begin{aligned} &-|x+1| \leq 0 \text { for every } x \in R\\ &-|x+1|+3 \leq 3 \text { for every } x \in R\\ \end{aligned}

Thus maximum value of f is attained when |x+1|=0

X = -1

So maximum value of f(x) = f(-1) = - |-1+1| + 3

So its maximum value is 3 and it does not have minimum value.
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