The number of points, at which the function
f(x) = | 2x + 1 | $-$ 3| x + 2 | + | x2 + x $-$ 2 |, x$\in$R is not differentiable, is __________.
Answer (integer)
2
Solution
$f(x) = |2x + 1| - 3|x + 2| + |{x^2} + x - 2|$<br><br>$$f(x) = \left\{ {\matrix{
{{x^2} - 7;} & {x > 1} \cr
{ - {x^2} - 2x - 3;} & { - {1 \over 2} < x < 1} \cr
{ - {x^2} - 6x - 5;} & { - 2 < x < {{ - 1} \over 2}} \cr
{{x^2} + 2x + 3;} & {x < - 2} \cr
} } \right.$$<br><br> $\therefore$ $$f'(x) = \left\{ {\matrix{
{2x;} & {x > 1} \cr
{2x - 3;} & { - {1 \over 2} < x < 1} \cr
{ - 2x - 6;} & { - 2 < x < {{ - 1} \over 2}} \cr
{2x + 2;} & {x < - 2} \cr
} } \right.$$<br><br>Check at 1, $-$2 and ${{ - 1} \over 2}$<br><br>Non. differentiable at x = 1 and ${{ - 1} \over 2}$
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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