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Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,0
Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,02 \end{array}\right.$ Is continuous at $x=2$, but not differentiable thereat.
CBSE | Class 12 | Differentiability | Exercise 10.1 | Maths | RD Sharma
Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,02 \end{array}\right.$ Is continuous at $x=2$, but not differentiable thereat.

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 8

Since, LHL = RHL = f (2)

Hence, F(x) is continuous at x = 2

Checking the differentiability at x = 2

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 9

$=> 5$

Since, (RHD at x = 2) ≠ (LHD at x = 2)

Hence, f (2) is not differentiable at x = 2.

i

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