Chapter P, Problem 9PS

(a)

To determine

To Calculate: The slope of the line joining the points $\left(2,4\right)$ and $\left(3,9\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=x^2$ at $\left(2,4\right)$.

(b)

To determine

To Calculate: The slope of the line joining the points $\left(2,4\right)$ and $\left(1,1\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=x^2$ at $\left(2,4\right)$.

(c)

To determine

To Calculate: The slope of the line joining the points $\left(2,4\right)$ and $\left(2.1,4.41\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=x^2$ at $\left(2,4\right)$.

(d)

To determine

To Calculate: The slope of the line joining the points $\left(2,4\right)$ and $\left(2+h,f\left(2+h\right)\right)$. Also verify that the slope obtained in part (a), (b), (c) of the line is same at $h=1,-1\text{ and }0.1$ respectively.

(e)

To determine

To Calculate: The slope of the tangent line at $\left(2,4\right)$ for the curve $f\left(x\right)=x^2$ and explain how the answer is obtain.