First slide

Differentiability

Question

$If f (x) = \{\begin{cases} - 3 x + 2, x < 1 \\ \frac{1}{2} x^{2} + 7, x \geq 1, \end{cases} then which of the following is not true$

Moderate

A

$f' (1 +) = 1$
B

$f' (1 -) = - 3$
C

$f' (1 -) = f' (1 +) = 1$
D

$is not differentiable at x = 1$

Solution

$\begin{array}{l} f^{'} (X) = \{\begin{aligned} - 3, & if x < 1 \\ x, if & x \geq 1 \end{aligned} \\ \Rightarrow f^{1} (1^{-}) = - 3, f^{1} (1^{+}) = 1 \end{array}$

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