$[-/12\mathrm{.}5$ Points$]$

LARCALC$121\mathrm{.}1\mathrm{.}008.$MI$.$

ASK YOUR TEACHER

Consider the function $f(x)=4x-x^2$ and the point $P(1,3)$ on the graph of $f.$

$($a$)$ Graph $f$ and the secant lines passing through $P(1,3)$ and $Q(x,f(x))$ for $x-$values of $2,1\mathrm{.}5,0\mathrm{.}5.$ Find the slope of each secant line. line passing through $Q(2,f(x))$

line passing through $Q(1\mathrm{.}5,f(x))$ line passing through $Q(0\mathrm{.}5,f(x))$

$($b$)$ Use the results of part $($a$)$ to estimate the slope of the tangent line to the graph of $f$ at $P(1,3).$

$$

Describe how to improve your approximation of the slope.

Choose secant lines that are nearly vertical.

Choose secant lines that are nearly horizontal.

Define the secant lines with points closer to $P.$

Define the secant lines with points farther away from $P.$