average rate of change

Question

f(x)=2/t; x=a, x=a+h

Answer 1

f(x) = 2/x

f(a) = 2/a

f(a+h) = 2/(a+h)

Compute lim(h-->0) the average rate of change lim(h-->0)[f(a+h)-f(a)]/h

= lim(h-->0) [2/(a+h)-2/a]/h

= lim(h-->0) [(2a-2(a+h))/a(a+h)]/h

= lim(h-->0) [(2a-2a-2h)/a(a+h)]/h

= lim(h-->0) [-2h/h(a(a+h))]

= lim(h-->0) [-2/a(a+h)]

Average rate of change of f(x)  is -2/a(a+h)