Chapter 11.3, Problem 73E

To determine

To evaluate: whether statement given as the slope of the graph of $y=x^2$ is different at every point on the graph of f is true or not.

Answer to Problem 73E

Yes, the statement is true. Slope is different at every point on the graph f .

Explanation of Solution

Given:

The slope of the graph of $y=x^2$ is different at every point on the graph of f

Calculation: -

Yes, the given statement is true.

For example

At (2, 4), finding the slope of $y=x^2$ ,

  $\begin{array}{c}y=x^2\\ \frac{dy}{dx}=2x\\ {\frac{dy}{dx}|}_{\left(2,4\right)}=2\times 2\\ =4\end{array}$

At (1, 1), finding the slope of $y=x^2$ ,

  $\begin{array}{c}y=x^2\\ \frac{dy}{dx}=2x\\ {\frac{dy}{dx}|}_{\left(2,4\right)}=2\times 1\\ =2\end{array}$

So, slope is different at every point on the graph f .