Find all points of inflection on the graph of the function .

Question

Find all points of inflection on the graph of the function  . ​

Quizplus · Accepted Answer

To find points of inflection, we need to find where the second derivative changes sign. Taking the first and second derivatives of the given function, we get:
f(x) = 11e^(-x/10)cos(x)
f'(x) = -e^(-x/10)(10cos(x) + sin(x))
f''(x) = e^(-x/10)(10sin(x) - 11cos(x))
Setting f''(x) = 0 and solving for x, we get:
10sin(x) - 11cos(x) = 0
tan(x) = 10/11
x = arctan(10/11) or x = arctan(10/11) + π
Plugging these values of x into the second derivative, we see that the sign changes from positive to negative at x = arctan(10/11) and from negative to positive at x = arctan(10/11) + π. Therefore, these are the points of inflection on the graph. The answer is D.

Find All Points of Inflection on the Graph of the Function