Question

Question attached as screenshot, choices are below. f is concave up from x = -1.5 to x = 1.5.f has an inflection point at x = 1.5.f has a relative minimum at x = 2.All of these are false.

Answer 1

Let's analyze each of the points.

f has a relative minimum at x = 2. (TRUE)

When a function's slope is zero at x, and the second derivative at x is: less than 0, it is a local maximum. greater than 0, it is a local minimum.

f is concave up from x = -1.5 to x = 1.5. (FALSE)

When it concaves up we're looking for when the second derivative is positive which means the slope of the first derivative is positive

f has an inflection point at x = 1.5. (TRUE)

So it's also the situation where we're going from negative to positive or for the first derivative is going from decreasing decreasing to increasing decreasing to increasing well