the height of two different projectiles after they are launched are modeled by f(X) and g(x). The function f(x) is defined as f(x)= -16x^2+42x+12. What is the approximate difference in the maximum height achieved by the two projectiles?

Question

anonymous · Answer

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anonymous · Answer

Do you know how to use derivatives?

anonymous · Answer

did you get the message I sent you

anonymous · Answer

A derivative of an equation allows you to find the slope of any line that is perpendicular to a curve at any position.  If you have not already learned this, please do not use the solution below:
$$f'(x)=-32x+42$$
The highest point would be where the slope of the perpendicular line is 0. 
$$f'(x)=0=-32x+42$$
$$x=\frac{42}{32}=\frac{21}{16}$$
Now plug the x=21/16 (where the projectile is at its highest point into the equation.
$$f(21/16)=633/16=39.56$$
That is the highest point for projectile following the equation f(x).

If there is another equation for g(x), follow the same method.

If it is only the table, I suppose you can take the highest point you see on the table and stick that into f(x) and then subtracting the results to get the difference in height.

anonymous · Answer

I'm not sure how far into math you are, so the solution I gave may not be acceptable for your case.  One solution you can do is to graph the formula they gave and then subtract the maximum value from your graph from the maximum value from the table they gave.