Chapter 16: Chapter 16

If \(A\) and \(B\) are constants, what is the relationship between $f(x)=A \cos x+B \sin x$ and its second derivative?

If the value of a stock price is given by \(p(t)=A \sin (\omega t+d)\) above yesterday's close for constants \(A \neq 0, \omega \neq 0\), and \(d\), where \(t\) is time, explain why the stock price is moving the fastest when it is at yesterday's close.

At what angle does the graph of \(f(x)=\sin x\) depart from the origin?

At what angle does the graph of \(f(x)=\cos x\) depart from the point \((0,1)\) ?

Evaluate the integrals. \(\int x \sin \left(3 x^{2}-4\right) d x\)

Find the derivatives of the given functions. \(s(x)=\left(x^{2}-x+1\right) \tan x\)

Graph the given functions or pairs of functions on the same set of axes. a. Sketch the curves without any technological help by consulting the discussion in Example \(1 .\) b. Use technology to check your sketches. \(f(t)=\cos (t) ; g(t)=5 \cos [3(t-1.5 \pi)]\)