But Dan, we all know that if
But he's asking for which is
Does this problem make anyones else's eyes bug out?
If f(x) = 1/(√x) find lim [f(x+h)-f(x)]/ h
h->0
b. If the above limit represents a slope function for the line tangent to f at (x, f(x)). Write the equation of the tangent line at x=4, in point-slope form.
Any line can be expressed in the form . The slope of the tangent line at a point (x, f(x)) of the graph is , so the slope of the tangent line is, in this case:
So we have the form:
Now, we know that the function f(x) and the tangent line have the same values at the point x = 4. So we know that
So I get that the tangent line to f(x) at x = 4 is .
-Dan