Question

What is the instantaneous slope of y =8/x at x = -3?


What is the average rate of change of y with respect to x over the interval [-3, 4] for the function y = 2x + 2?

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 2.


I am a little confused here can anyone show the work and steps please.

Answer 1

y = 8/x
y' = -8/x^2
now plug in x = -3

the avg rate of change is

change in y
------------------
change in x

So, that would be

(y(4)-y(-3))/(4-(-3))
Now just plug in the numbers

Answer 2

i have no idea

Answer 3

kjbujbh;