Three problems:
1) find the slope of the tangent line for the graph f(x)= x^2 at (2,4).
2) Find the slope of the line joining (2,4) and (2+h, f(2+h)) in terms of the nonzero number h. (This is also for the graph f(x)= x^2)
And
A rancher has 300 feet of fence to enclose two adjacent pastures. (See figure) Express the total area A of the two pastures as a function of x. What is the domain of A?
Graph the area function (I suppose I can do this once I find the equation) and estimate the dimensions that yield the maximum amount of area for the pastures.
Find the dimensions that yield the maximum amount of area for the pastures by completing the square.
THANKS for reading this and trying to help
Let the slope of the line be m.
Find
Spoiler:
Consider the perimeter of the fence.
Rearrange for y
Now Area as there are 2 pastures
Now graph this function. It is a quadratic so you can find the turning point (or the maximum) using symmetry.