- #1
PsychonautQQ
- 784
- 10
Homework Statement
Q: Does the graph of f(x) = x^(1/2) have a point of tangency with the line y = (x/4) + 1?
Homework Equations
lim x->a (f(x) - f(a)) / (x-a)
The Attempt at a Solution
If the limit exists of the relevant equation than there is a point of tangency.
So I'm having a bit of trouble proving anything here...
using the equation I come to
lim x->a (x^(1/2) - (x/4) + 1) / (x-a)
which looks like as x goes to a the denominator will approach zero which leads me to believe it diverges to infinity? does that mean the limit doesn't exist?
When setting the equations equal to each other I find that they intersect at (4,2). Do I plug 4 in for a? same thing happens except this time the numerator obviously approaches zero as well...