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

is always

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

is never

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

need not be

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

Open in App

Solution

The correct option is C need not be
A function is differentiable at a point if and only if the left and right derivates are finite and equal, and it is continuous at that point. Hence, f(x) is differentiable at a if it is continuous. Otherwise, it is non-differentiable.

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. Consider the following statements:

1.

Derivative of

f (x)

may not exist at some point.

2.

Derivative of

f (x)

may exist finitely at some point.

3.

Derivative of

f (x)

may be infinite (geometrically) at some point.
Which of the above statements are correct?

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.

Join BYJU'S Learning Program

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

The correct option is C need not beA function is differentiable at a point if and only if the left and right derivates are finite and equal, and it is continuous at that point. Hence, f(x) is differentiable at a if it is continuous. Otherwise, it is non-differentiable.

The correct option is C need not be
A function is differentiable at a point if and only if the left and right derivates are finite and equal, and it is continuous at that point. Hence, f(x) is differentiable at a if it is continuous. Otherwise, it is non-differentiable.