Q. 4 - Calculus

Question

Sketch a graph of $f\left(x\right)=x^2$, and sketch the lines that point in the direction of the curve at $(0, f(0\left)\right), (2, f(2\left)\right)$, and $(4, f(4\left)\right)$. Relate the slopes of these lines to the answers to the last three exercises.

Step-by-Step Solution

Answer

The graph is as follows,

The slopes of the lines are the derivative of the given function at points $x=0,2,4$.

Step 1. Given Information.

We are given a function,

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

Step 2. Sketching the graph.

The graph for $(0,f(0\left)\right)$ is as follows,

The graph for $(2,f(2\left)\right)$ is as follows,

The graph for $(4,f(4\left)\right)$ is as follows,

Step 3. Relation with exercises.

Above lines are actually tangent to the curve $x^2$ at $x=0,2,4$ and the derivative of $x^2$ at $x=0,2,4$ will give the slope at points.