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.

True

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

False

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

Open in App

Solution

The correct option is A True
Fit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at $x_{0}$ .

For example, consider the function $f (x) = \frac{x^{2}}{x}$ .

LHD at x=0 is 1

RHD at x=0 is 1

But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0

Suggest Corrections

Similar questions

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. 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.

If the function f(x) has LHD and RHD at x₀, which are finite and equal, then f(x) is differentiable at x₀, always.

Q. If both f(x) and g(x) are differentiable functions at

x = x_{0}

, then the function defined as h(x) = maximum {f(x), g(x)} :

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.

Join BYJU'S Learning Program

If the function f(x) has LHD and RHD at x0, which are finite and equal, then f(x) is differentiable at x0, always.

The correct option is A TrueFit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at x0. For example, consider the function f(x)=x2x. LHD at x=0 is 1 RHD at x=0 is 1 But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0

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.