Question

Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0 < x < 3

Answer 1

Inflection points are points for which the second derivative of the function vanishes and changes sign.

Let us consider the function f. The second derivative of f is given by:

"()sin(3 - cos(), 0< x < 3

Plotting the above function in the interval (0,3) we get the following graph:

1.0 0.5 0.5 1,0 2.0 1,5 3.0 -0.5 -1.0

As you can see at 5 places the second derivative becomes zero and changes sign.

Therefore, there are five inflection points for the function f.