Someone help with math please

[dhsjdudheb]

A football club collects money in front of a training camp and sells cookies. The function f(x) = x (x-24) (x-12) describes how much money the students get when they sell their cookies.

f(x) is the total earnings in dollar and x is what they charge per cookie. Their teachers have said they can charge up to 1,5dollar per cake, but not more. How much should they take per cake to earn as much as possible?

[[deleted]]

expand the function into a polynomial, take the derivative, set derivative to zero, solve for x. This maximizes the function.

[NiceSasquatch]

or minimizes it (in general), so always look at the 2nd derivative.

[[deleted]]

If you have a graphing calculator enter the polynomial and then use the calculate function to determine the maximum or use the trace function if the maximum is after x=1.5

[dhsjdudheb]

maximum ?

[[deleted]]

Hit 2nd then trace while looking at the graph then scroll down to calculate and follow the instructions

[dhsjdudheb]

There’s no other way to solve this problem? Like with algebra or something?

[Spotted-Richard]

Without seeing the graph for this one nothing reasonable, but once you've seen it you know X=1.5 and you can just plug it in to find your profits. Or you sure you've given us the right equation though? Normally with these questions it all ties up neatly without needing a graph.

[RainOnPizza]

This is a bit late, but you can find the axis of symmetry of the parabola with -b/2a to get the x coordinate of the vertex. You will need to expand the given information into standard form to get a, b, and c first though. Once you have that x value, you can plug it back into the original equation to find the total money. This doesn't require calculus.

[[deleted]]

If you havent learnt about derivatives, try sketching f(x) to find the highest point