You visited us 1 times! Enjoying our articles? Unlock Full Access!

Critical Point

If a function...

Question

If a function $f (x)$ is differentiable at $x = c$ then it is continuous a $x = c$ .

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
A function $f (x)$ is differentiable at $x = c ⟺ f (x)$ is continous at $x = c$

Suggest Corrections

Similar questions

f (x) = {\begin{matrix} x^{2} & for x \leq c a x + b & for x > c \end{matrix}

f (x)

x = c

a = 2 c

b = - c^{2}

\to

_{0}

_{0}

_{0}

_{0}

_{0}

_{0}

f (x) = ⎧ ⎨ ⎩ \begin{matrix} | x | + 3 & \forall x \leq - 3 - 2 x & \forall - 3 < x < 3 6 x + 2 & \forall x \geq 3 \end{matrix}

- 3 \leq x < 3

x > 3

x = 3

{lim}_{x \to a} f (x) = f (a)

f (x)

x = a

x = a

f (x)

x = 0

f (x) = {sin}^{- 1} (cos x)

f (x) = |\log_{e} | x ||

Join BYJU'S Learning Program