§2.2 The sine and cosine functions (continued)

Summary

For $f(x) = 3\cos(x) - 2\sin(x) + 6$, the tangent line approximation at $a = \pi$ is

For the same $f(x) = 3\cos(x) - 2\sin(x) + 6$, at $x = \frac{\pi}{2}$ the function is

An investment has value $V(t) = 24 \cdot 1.07^t + 6\sin(t)$ thousand dollars and satisfies $V''(2) \approx -5.33$. At $t = 2$ this says the rate of change of the portfolio is itself

For $f(x) = 3\cos(x) - 2\sin(x) + 6$, compute $f'(\frac{\pi}{4})$ rounded to three decimals.

With $V(t) = 24 \cdot 1.07^t + 6\sin(t)$ in thousands of dollars, compute $V'(2)$ rounded to three decimals.

The formula $\frac{d}{dx}[\sin(x)] = \cos(x)$ holds for every real number $x$.