Question

Use the alternate definition, lim x->a f(x)-f(a)/x-a, to determine the instantaneous rate of change of f(x)= 1/x at the point (1,1/5)

a)1/5
b)-1/5
c)1/25
d)-1/25

Answer 1

just apply the definition. What's the problem?

f(x) = 1/x
f(a) = 1/a
f(x)-f(a) = (a-x)/(ax)
Now divide that by x-a and you have -1/(ax)
the limit as x->a is -1/x^2

So, fix your typo and adjust the evaluation.

(1,1/5) is not on the curve for 1/x.