§2.4 Derivatives of other trigonometric functions (continued)

Summary

An object moving vertically has its height at time $t$ (measured in feet, with time in seconds) given by the function $h(t) = 3 + \frac{2\cos(t)}{1.2^t}$. - What is the object's instantaneous velocity when $t =2$? - What is the object's acceleration at the instant $t = 2$? - Describe in everyday language the behavior of the object at the instant $t = 2$.

Let $f(x) = \sin(x) \cot(x)$. - Use the product rule to find $f'(x)$. - True or false: for all real numbers $x$, $f(x) = \cos(x)$. - Explain why the function that you found in (a) is almost the opposite of the sine function, but not quite. (Hint: convert all of the trigonometric functions in (a) to sines and cosines, and work to simplify. Think carefully about the domain of $f$ and the domain of $f'$.)

Let $p(z)$ be given by the rule

. - Determine $p'(z)$. - Find an equation for the tangent line to $p$ at the point where $z = 0$. - At $z = 0$, is $p$ increasing, decreasing, or neither? Why?