Take the formula for the slope between two points.
Then just input your value for x.
I think you'll find the slope does exist, and is not some huge number. 3.99 is not equal to 4, and you'll also see that the numerator is rather small as well. That's very typical of secant/tangent lines to smooth curves. You're always dealing with slopes that look like, or are close to, 0/0.