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

$f^{1} (1 +) = 1$
B

$f^{1} (1 -) = - 3$
C

$f^{1} (1 -) = f^{1} (1 +) = 1$
D

$f is not differentiable at x = 1$

Solution

$f^{1} (x) = \{\begin{cases} - 3, if x < 1 \\ x, if x \geq 1 \end{cases}$

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