Question

f(x)=2x^3-x^2-20x-7
Where is x both increasing and concave down?

Answer 1

If this is a calculus based question:

The first derivative tells you where on the graph are increasing and decreasing. Find your zero's from the equation of the first derivative, and draw a number line like so:


Mark where your zeros are, and plug in numbers in between the areas. You don't necessarily have to solve it entirely, just know whether it is positive or negative in the region. If it's positive, it's increasing. Negative, decreasing.

The second derivative tells you the concavity of the graph. You can use the same method as above to find areas where is positive, concave up; negative, concave down.

Answer 2

However, if this isn't a calculus question, are you able to graph the equation to see which ares are increasing, concave down? Or are you expected to know how to graph and solve for the regions that are asked?

Answer 3

@Yvonmei is this a calculus based question or not?