Question

State whether the given statement is True or False.

The derivative of a function is defined at $a$, provided $li{m}_{h\to 0}\frac{f(a+h)-f\left(a\right)}{h}$ exists.

• A. True
• B. False

Answer 1

The correct option is A True

Consider the given function as $f\left(x\right)$
Then, its derivative at a point $a$ is $f^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{f(a+h)-f\left(a\right)}{h}$ wherever the limit exists.
Hence, the derivative of a function is defined provided the limit exists.
Therefore, the given statement is true.