Q. 1 - Calculus

Question

Calculate the derivative of $f\left(x\right)=x^2$ at $c=0$.

Step-by-Step Solution

Answer

The derivative is $0$.

Step 1. Given Information.

We are given a function,

$f\left(x\right)=x^2$

Step 2. Finding the derivative.

The derivative is given by,

$$\begin{gathered} f^{\text{'}}\left(c\right)=\underset{h\to 0}{\lim }\frac{f(c+h)-f\left(c\right)}{h} \\ {f}^{\text{'}}\left(0\right)=\underset{h\to 0}{\lim }\frac{(0+h{)}^2-(0{)}^2}{h} \\ =\underset{h\to 0}{\lim }\frac{h^2}{h} \\ =\underset{h\to 0}{\lim }h \\ =\underset{h\to 0}{\lim }0 \\ =0 \end{gathered}$$