Final answer:
The point of inflection is where the concavity changes. To find it, set the second derivative of the function equal to zero. The function is concave upward when the second derivative is positive, and concave downward when the second derivative is negative.
Step-by-step explanation:
The function has a point of inflection at the point where the concavity changes. At this point, the function changes from being concave upward to concave downward, or vice versa. To find the point of inflection, we can set the second derivative of the function equal to zero and solve for the x-value. This will give us the x-coordinate of the point of inflection.
To determine the intervals where the function is concave upward or concave downward, we can look at the sign of the second derivative of the function. If the second derivative is positive, the function is concave upward. If the second derivative is negative, the function is concave downward.
For example, if the second derivative is positive on the interval (a,b), then the function is concave upward on that interval. If the second derivative is negative on the interval (c,d), then the function is concave downward on that interval.