Question

Calculate the average rate of change of the given function f over the intervals [a, a+h] where h=1, 0.1, 0.01, 0.001, and 0.0001.
I have no clue how to do this. Any help would be appreciated. Thanks

I know I use the formula

f=f (a+h) - f (a)/h

Then do I need to plug in
the -2x - (3x^2)
of just plug the zero in for the x?


f(x)= 3x^2 -2x ; a=0

Answer 1

f(a) = 3a^2-2a
f(a+h) = 3(a+h)^2 - 2(a+h)
= 3a^2 + 6ah + 3h^2 - 2a - 2h

f(a+h)-f(a) = 6ah + 3h^2 + 2h
So,

(f(a+h)-f(a))/h = 6a + 3h + 2

So, with various values of h,
f(a+1) = 6a+3+2
f(a+0.1) = 6a + 0.3 + 2 = 6a + 2.03
and so on. Nothing difficult, just algebra I.