Exercise 5

Let $f(x) = 3\cos(x) - 2\sin(x) + 6$.

1. Determine the exact slope of the tangent line to $y = f(x)$ at the point where $a = \frac{\pi}{4}$.

2. Determine the tangent line approximation to $y = f(x)$ at the point where $a = \pi$.

3. At the point where $a = \frac{\pi}{2}$, is $f$ increasing, decreasing, or neither?

4. At the point where $a = \frac{3\pi}{2}$, does the tangent line to $y = f(x)$ lie above the curve, below the curve, or neither? How can you answer this question without even graphing the function or the tangent line?