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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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

Suggest Corrections

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

x_{0}

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

x_{0}

, always.

Q. Given the following statements about a function f: R

\to

R, select the right option.

P : If f(x) is continuous at x = x

_{0}

, then it is also differentiable at x = x

_{0}

Q : If f(x) is continuous at x = x

_{0}

, then it may not be differentiable at x = x

_{0}

.

R : If f(x) is differentiable at x = x

_{0}

, then it is continuous at x = x

_{0}

Join BYJU'S Learning Program

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.