Rita has 360 meters of fencing and wishes to enclose a rectangular field. Suppose that a side length (in meters) of the field is x, as shown below. X (a) Find a function that gives the area 4 (x) of the field (in square meters) in terms of x. 4(x) = (b) What side length x gives the maximum area that the field can have? Side length x : meters (c) What is the maximum area that the field can have? Maximum area: square meters

Given: f(x)=10x-x^2; find f(5)=____?

Find the point on the graph of the function f that is closest to the point (a, b) by minimizing the square of the distance from the graph to the point. f(x) = 8x+3 and the point (-5, 3)

Find the inflection point (x,, f(x,)) of the following function: f(x) = 3x³ + 9x² – x + 11. If - an inflection point does not exist, enter DNE for both answers. Xp = %D f(xp) = Check

Find values of f(x)=In(x+3)+3: domain? range? asymptote? y-intercept? x-intercept?

The height of a punted football can be modeled by the function: f(x) = -.0079 x2 + 1.8x + 1.5. In this equation, f(x) is the height in feet, and x is the horizontal distance, also in feet, from the point the ball is punted. Using that function answer this:  How high is the ball when it is punted? What is the maximum height of the punt?  Consider what the height would be if you changed x (the horizontal distance). Plug in some values for x to see how the height changes.

Suppose that f(x)=√8-2x  Find the value of : f(-14)

You are building a greenhouse next to your house, as shown in the figure. Because the house will be used for one side of the enclosure, only three sides will need to be enclosed. You have 60 feet of fiberglass to enclose the three walls. The function f(x) = x(60 - 2x) describes the area of the greenhouse that you can enclose, f(x), in square feet, if the width of the greenhouse is x feet. Solve, as shown.

The height, h(x), of a punted rugby ball is given by h(x)= 21 -x+3 where x is the horizontal distance 32 64 in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point? 45 feet 26 feet 24 feet 31 feet 21 feet