Chapter 1.PS, Problem 8PS

To determine

(a)

To find:

The average rate of change of the function $f\left(x\right)=-x^2+4x-3$ for $x_1=1,x_2=2$.

To determine

(b)

To find:

The average rate of change of the function $f\left(x\right)=-x^2+4x-3$ for $x_1=1,x_2=1.5$.

To determine

(c)

To find:

The average rate of change of the function $f\left(x\right)=-x^2+4x-3$ for $x_1=1,x_2=1.25$.

To determine

(d)

To find:

The average rate of change of the function $f\left(x\right)=-x^2+4x-3$ for $x_1=1,x_2=1.125$.

To determine

(e)

To find:

The average rate of change of the function $f\left(x\right)=-x^2+4x-3$ for $x_1=1,x_2=1.0625$.

To determine

(f)

To find:

The average rate of change is approaching one value. If it is approaching one value, then find the value.

To determine

(g)

To find:

The equations of the secant lines through the points $\left(x_1,f\left(x_1\right)\right)$ and $\left(x_2,f\left(x_2\right)\right)$ for part (a)-(e).

To determine

(h)

To find:

The equation of the line through the point $\left(1,f\left(1\right)\right)$ using the answer from part (f) as the slope of the line.