Let $f(x)=x^3-x^2-x.$

a$.$ Find the slope of the secant line between $x=1$ and $x=0\mathrm{.}999.$

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Substitute for $x$

Expandf

Simplify to get point coordinates $($use color $1$ for point $1,$ color $2$ for point $2,$ and color $3$ form$\_$sec$)$

simplify to get the secant slope $($use color $3$ for slope information$)$Date

b$.$ Sketch the graph of $f(x),$ label the two points in question, sketch the secant line between the two points, and label the secant slope. $($Color$-$code to match part $($a$).)$

c$.$ Estimate the slope of the tangent line based on your answer for the slope of the secant line in part $($a$).$ Sketch the graph of $f(x),$ label the coordinates of the point at $x=1,$ sketch the tangent line, and label the tangent line slope. $($Color$-$code to match part $($a$).)$

d$.$ Explain why your answer for slope reasonable based on an attribute of the graph. BONUS for basing it on two attributes of the graph.