6) A function y =e-2x is defined numerically for some data range x. It can be entered using: (а) у - ехp(-x) * еxp(-х) (b) y= sqr(exp(-xr)) (c) у - еxp(-x). * еxp(-x) (d) y = sqrt(exp(-x))

Find the derivative

An economist is interested in how the price of a certain item affects its sales. When the price of the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand") Suppose we found out that f(150) = 2,000 and that f'(150) = -25. (a) Sketch the information of two boldface statements in a quick picture/sketch: (b) Write out in words what the first statement f(150) = 2,000 means in the context. (c) The fact that the derivative is negative reflects what natural phenomenon? (d) Write out in words what the statement f'(150) = -25 means in the context. (Add in appropriate units!) (e) Use the information given to estimate f(151) and f(149.5). Show your work, and explain your rationale for proceeding as you did. A little picture would be ideal to explain your thinking.

You have a 20-meter length of wire. An x meter length is cut from the end of the wire, and is formed into a circle. The remaining portion of the wire is formed into a square.  a) Write an expression for A (x), the total are (in m^2) of the the circle and the square together, as a function of x.  b) Suppose that the area of the square may be no greater than 5m^2. Under these conditions, what is the domain of the function A (x)? Give an exact awnser.