For the function f(x)=x^2-4x:

Question

1.For the function f(x)=x^2-4x:
 
a.Determine the average rate of change from x=1 to x=4

   b. Determine the instantaneous rate of change at x=1.

Answer 1

a. The rate of change is given by f'(x)=2x-4. The average rate of change if (f'(4)+f'(1))/2=(4-2)/2=1. 2x-4 is a linear function, and if we take integer values of x and average them we get: (-2+0+2+4)/4=1. If we increment x by 0.5 steps we get: (-2-1+0+1+2+3+4)/7=1, and so on.

b. Instantaneous change of direction at x=1 is -2.