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.

True

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False

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Solution

The correct option is B False
For f(x) to be differentiable at x₀, the

LHD, ${lim}_{△ \to 0} \frac{f (x + △ x) - f (x)}{△ x}$ and

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

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

Intestively whenever there is a sharp edge 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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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.

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.