SOLUTION: Provide a sketch of any function that has the following properties a. x intercepts at: (-3,0), (0,0), (4,0) b. Concave up on the intervals (−∞, 0)𝑈(1,2) c. Concave down o

Question 1163581: Provide a sketch of any function that has the following properties
a. x intercepts at: (-3,0), (0,0), (4,0)
b. Concave up on the intervals (−∞, 0)𝑈(1,2)
c. Concave down on the intervals(0,1)𝑈(2, ∞)
d. Local min at (-2,-4)
e. Local max at (2,5)
f. Point of inflection at (1,3).
Thank you I can't quite figure out this question.
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

It's not surprising you can't figure this one out; the instructions are not clear.

It appears to be looking for a polynomial function; but that is not specified.

And it is a good thing that a polynomial function is not specified, because there is no polynomial function that has all those characteristics.

Also, the problem doesn't ask you to define a function with all the stated characteristics -- it only asks you to sketch one. That we can do.

So, starting from -infinity and moving to the right....

(1) Concave up on (-infinity,0), with zeros at (-3,0) and (0,0) and a local minimum at (-2,-4)
That part could be a polynomial.

(2) Concave down on (0,1); concave up on (1,2), with a point of inflection at (1,3)

All that could also be a polynomial.

Since the concavity changed at (0,0), there is a point of inflection there -- although that is not stated in the given information.

(3) local maximum at (2,5); concave down on (2,infinity).

Here we can't have a polynomial. In a polynomial, the concavity does not change at a local maximum or local minimum. But the specifications say the function is concave up to the left of the local maximum and concave down to the right.

And of course it is easy for the function to be concave down everywhere to the right of 2.

So we can sketch a function with all the given characteristics -- but it will not be a polynomial function.

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