Given f(x) is continuos at $x_{0}$ , for f(x) to be differentiable at $x_{0}$ , the left hard Derivative and the right hand Derivative must exist finitely.

True

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False

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Solution

The correct option is B
False

For f(x) to be differentiable at $x_{0}$ , the

$L H D, lim △ x \to 0 \frac{f (x + △ x) - f (x)}{△ x}$ and

$R H D, lim △ x \to 0 \frac{f (x + △ x) - f (x)}{△ x}$ must be finite and equal.

For example, the graph f(x) has LHD and RHS are not equal.

Intestively whenever there is a sharp ede on f(x) the LHD and RHD are not equal and f(x) wont be

differentiable at x0 even though given f(x) is continuous

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Similar questions

Given f(x) is continuos at $x_{0}$ , for f(x) to be differentiable at $x_{0}$ , the left hard Derivative and the right hand Derivative must exist finitely.

Q. Given f(x) is continuos at x₀, for f(x) to be differentiable at x₀, the left hard Derivative and the right hand Derivative must exist fanitely.

Q. The left and right derivatives of a function f(x) exist finitely and are equal at a point a. f(x) differentiable at a.

Q. If the function f(x) has LHD and RHD at

x_{0}

, which are finite and equal, then f(x) is differentiable at

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, always.

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Given f(x) is continuos at x0, for f(x) to be differentiable at x0, the left hard Derivative and the right hand Derivative must exist finitely.

Given f(x) is continuos at $x_{0}$ , for f(x) to be differentiable at $x_{0}$ , the left hard Derivative and the right hand Derivative must exist finitely.