Exercise 1

Compute the derivative function of $f(x)=x^3-2x^2+1$ at the points $x=-1$, $x=0$ and $x=1$. Explain your result. Find an equation of the tangent line to the graph of $f$ at each of the three given points.

Exercise 2

The pH measures the concentration of hydrogen ions H$^+$ in an aqueous solution. It is defined by \[ \mbox{pH} = -\log_{10}(\mbox{H}^+). \] Compute the derivative of the pH as a function of the concentration of H$^+$. Study the growth of the pH function.