Question

Below is the graph of f’(×), the derivative of f(x), and has x-intercepts at x =-3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5.Which of the following statement is false?

Answer 1

Option 1:

Explanation:

In order for f(x) to be concave up in an interval, the graph of the derivative would have to be increasing in that interval.

In the given graph, from x=-1.5 to x=1.5, the graph of the derivative is decreasing, therefore, the statement that "f is concave up from x=-1.5 to x=1.5" is false.

Next, for f to have an inflection point at any x-value the slope of the derivative, f'(x) must change signs at that x-value. Therefore, the statement "f has an inflection point at x=1.5" is true.

Finally, for f(x) to have a relative minimum at x=2, the value of the derivative must be 0, which is as seen on the graph.

Therefore, the first option is False.