Q. 3TF - Calculus

Question

Use the limit you just found to calculate the exact slope of the tangent line to $f\left(x\right)=x^2$ at $x=4$. Obviously you should get the same final answer as you did earlier.

Step-by-Step Solution

Answer

The value of slope is 8.In the previous case we also get the slope value as 8.

Step 1.Given Information

Given equation $f\left(x\right)=x^2$ at $x=4.$

Step 2.Finding the slope value

The derivative formula $$\begin{gathered} f^{\text{'}}\left(c\right)=\underset{z\to c}{\lim }\frac{f\left(z\right)-f\left(c\right)}{z-c} . \\ =\underset{z\to 4}{\lim }\frac{z^2-4^2}{z-4} \\ =\underset{z\to 4}{\lim }\frac{(z+4)\cancel{\left(z-4\right)}}{\cancel{\left(z-4\right)}} \\ =(4+4) \\ =8 . \end{gathered}$$ 

Step 3.The solution

The value of slope is 8.In the previous case we also get the slope value as 8.