Consider the function f(x) = 2 x + 7 on the interval 2, 7. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (2, 7) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

If xis large, which function grows faster, f(x)=2x or g(x)=x2?

Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.