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Exercise 10.1

Discuss the continuity and differentiability of the function f (x) = |x| + |x -1| in the interval of (-1, 2).

CBSE, Class 12, Differentiability, Exercise 10.1, Maths, RD Sharma

Since, a polynomial and a constant function is continuous and differentiable everywhere => f(x) is continuous and differentiable for x ∈ (-1, 0) and x ∈ (0, 1) and (1, 2). Checking continuity...

Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,0<x \leq 1 \\ 2 x^{2}-x, 1<x \leq 2 \\ 5 x-4, x>2 \end{array}\right.$ Is continuous at $x=2$ , but not differentiable thereat.

CBSE, Class 12, Differentiability, Exercise 10.1, Maths, RD Sharma

Since, LHL = RHL = f (2) Hence, F(x) is continuous at x = 2 Checking the differentiability at x = 2 $=> 5$ Since, (RHD at x = 2) ≠ (LHD at x = 2) Hence, f (2) is not differentiable at x =...

$\text { Show that } f(x)=\left\{\begin{array}{c} 12 x-13, \text { if } x \leq 3 \\ 2 x^{2}+5, \text { if } x>3 \end{array} \text { is dif ferentiable at } x=3 . \text { Also, find } f^{\prime}(3)\right.$

CBSE, Class 12, Differentiability, Exercise 10.1, Maths, RD Sharma

checking differentiability of given function at x = 3 => LHD (at x = 3) = RHD (at x = 3) = 12 Since, (LHD at x = 3) = (RHD at x = 3) Hence, f(x) is differentiable at x = 3.

Show that f (x) = ${{x}^{\frac{1}{3}}}$ is not differentiable at x = 0.

CBSE, Class 12, Differentiability, Exercise 10.1, Maths, RD Sharma

Since, LHD and RHD does not exist at x = 0 Hence, f(x) is not differentiable at x = 0

Show that f (x) = |x – 3| is continuous but not differentiable at x = 3.

CBSE, Class 12, Differentiability, Exercise 10.1, Maths, RD Sharma

Discuss the continuity and differentiability of the function f (x) = |x| + |x -1| in the interval of (-1, 2).

Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,0<x \leq 1 \\ 2 x^{2}-x, 1<x \leq 2 \\ 5 x-4, x>2 \end{array}\right.$ Is continuous at $x=2$ , but not differentiable thereat.

$\text { Show that } f(x)=\left\{\begin{array}{c} 12 x-13, \text { if } x \leq 3 \\ 2 x^{2}+5, \text { if } x>3 \end{array} \text { is dif ferentiable at } x=3 . \text { Also, find } f^{\prime}(3)\right.$

Show that f (x) = ${{x}^{\frac{1}{3}}}$ is not differentiable at x = 0.

Show that f (x) = |x – 3| is continuous but not differentiable at x = 3.

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Discuss the continuity and differentiability of the function f (x) = |x| + |x -1| in the interval of (-1, 2).

Show that the function is defined as follows Is continuous at , but not differentiable thereat.

Show that f (x) = is not differentiable at x = 0.

Show that f (x) = |x – 3| is continuous but not differentiable at x = 3.

Show that the function $f$ is defined as follows $f(x)=\left\{\begin{array}{c} 3 x-2,0<x \leq 1 \\ 2 x^{2}-x, 1<x \leq 2 \\ 5 x-4, x>2 \end{array}\right.$ Is continuous at $x=2$ , but not differentiable thereat.

Show that f (x) = ${{x}^{\frac{1}{3}}}$ is not differentiable at x = 0.