Q. 3 - Calculus

Question

Explain why it is not a simple task to calculate the slope of the tangent line to a function $f$ at a point $x=c$. Shouldn’t calculating the slope of a line be really easy? What goes wrong here?

Step-by-Step Solution

Answer

The slope of the tangent at $x=c$ is not easy to determine because exact value of slope of the tangent can't be determined correctly.

Step 1. Given information

Given a function $f\left(x\right)$.

Step 2. Explanation

The slope of a function at any point $x=c$, is the approaches of rate of change of $f\left(x\right)$ with respect to  $x=c$ and its nearby points. Since it is just an approach, therefore exact value of slope of the tangent can't be determined correctly. But for any nearby point at $x=c+h$ to $x=c$, if $h\to 0$ the slope of the tangent is approximate.