Problems of Derivatives

Exercise 1

Compute the derivative function of $f (x) = x^{3} - 2 x^{2} + 1$ 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.

Solution

f^{'} (- 1) = 7

f^{'} (0) = 0

f^{'} (1) = - 1

.
Tangent line at

x = - 1

y = - 2 + 7 (x + 1)

.
Tangent line at

x = 0

y = 1

.
Tangent line at

x = 1

y = - (x - 1)

Exercise 2

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

Solution

The pH decreases as the concentration of hydrogen ions H

^{+}

increase.

Derivatives

Last updated on Sep 15, 2020