10.4 Homework MAT 210

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. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) (Round your answers to seven decimal places.)

f(x)=x^2/8 ; a1

h = 1 

h = 0.1

h = 0.01

h = 0.001

h = 0.0001

Answer 1

Average rate of change of f(x) equals [f(a+h)-f(a)]/h

a=1,h=1, [f(1+1)-f(1)]/1 = [(1+1)²/8-1/8]/1 = .375

a=1, h=.1, [f(1+.1)-f(1)]/.1 = [(1+.1)²/8-1/8/.1] = .2625

a=1, h=.01, [f(1+.01)-f(1)]/.01 = [(1+.01)²/8-1/8]/.01 = .25125

a=1, h=.001, [f(1+.001)-f(1)]/.001 = [(1+.001)²/8-1/8]/.001 = .250125

a=1, h=.0001, [f(1+.0001)-f(1)]/.0001 = [(1+.0001)²/8-1/8]/.0001 = .2500125