Question

Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)f(x) = x + 9 cos x, [0, 2]

Answer 1

Answer with explanation: We need to determine the points where the function changes sign, the provided function:

$f(x)=x+9\cos (x)$

The inflation points are at the following x values:

$\begin{gathered} x\Rightarrow\frac{\pi}{2}+2\pi n \\ x\Rightarrow\frac{3\pi}{2}+2\pi n \end{gathered}$

$\begin{gathered} n=1 \\ x=\frac{5}{2}\pi \\ y=f(x)=\frac{5}{2}\pi+9\cos (\frac{5}{2}\pi) \end{gathered}$