European Sens said:If n is a positive integer, how many times does the function f(x) = x^2 + 5cosx change concavity in the interval 0 <= x <= 2*pi*n?
A) 0
B) 1
C) 2
D) n
E) 2n
Why is that so?European Sens said:I think its E.
A change in concavity of a function refers to a change in the direction of the curvature of the graph of the function. It can be either a change from concave up to concave down, or vice versa.
The concavity of a function is determined by the second derivative of the function. If the second derivative is positive, the function is concave up, and if the second derivative is negative, the function is concave down.
A point of inflection is a point on the graph of a function where the concavity changes. It marks the transition from concave up to concave down, or vice versa.
A change in concavity can indicate a change in the behavior of the function. It can also help to identify key points on the graph, such as local maxima or minima.
A change in concavity can result in a change in the shape of a function's graph. For example, a change from concave up to concave down can result in the function having a point of inflection or a local maximum or minimum.