Work the problems below on a sheet of paper, making sure to show all of your work. Upload a picture or $.$pdf of the work to the Written Homework $1$ drop box in D$2$L$.$

Let $f(x)=2x^2-1$

Compute and simplify the difference quotient $\frac{f(1x)-f(1)}{x}.$

Find the slopes of the secant lines at $x=1$ corresponding to $x=0\mathrm{.}1,0\mathrm{.}01,0\mathrm{.}001.$

Make a guess for the slope of the tangent line at $x=1.$

Find the equation of the tangent line at $x=1.$

Sketch the graph of $y=f(x)$ and the tangent line found in problem $4.$