what is the length? (24 - 2x), since we take the side that is 24 inches and fold away x inches from one side and x inches from the other.
what is the width? (24 - 4x), since we take a side that is 24 inches and fold away 2x from each side.
what is the height? this is simply x, for obvious reasons.
multiply those and simplify to get the volume.
the domain of a function is the set of input values (in this case, x-values) for which the function is defined. this is a polynomial, what is the domain for all polynomials?(b) Determine the domain of function V.
find the x- and y-intercepts. after finding the x-int, divide the x-axis into regions with the intercepts as the dividing line. test x-values from each region to see whether the graph is above the x-axis or below the x-axis.(c) Sketch a graph of the function
also, find the end behavior. one end will go to infinity, while the other goes to -infinity. which which end does which. after this, you will be able to draw the graph (it will be in the general shape of an graph. you should know what that looks like, if you don't, look it up)
how accurate does your estimate have to be? are you allowed to use calculus?and estimate the
value of x for which V(x) is is maximum.