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Answer:
1. f has an inflection point at x = -1.5
Explanation:
Let's analyze each statement given.
1. f has an inflection point at x = -1.5 --> TRUE
An inflection point is a point in which the function f(x) changes concavity: this means that the first derivative of a function has a relative minimum or maximum, and therefore the second derivative is zero, .
In this case, we see that at the point
x = -1.5
The first derivative is flat: this means that at this point, the second derivative is zero, so this is an inflection point.
2. f is increasing on the interval from x = -3.2 to x = -4.5. --> FALSE.
We simply don't know this: in fact, we cannot see the graph of the derivative between -4.5 and -3.2, therefore we don't know if the function is increasing or not.
3. f has a relative minimum at x = 1.5 --> FALSE.
A function has a relative minimum at a point
if the first derivative
is zero at that point:
and moreover, the derivative is negative on the left of the point and positive on the right of the point.
This is not the case: in fact, we see that at x = 1.5 the first derivative is not zero, therefore this statement is not true.