There are two functions f(x)=x^2 and g(x)=x^3 they intersect at (1,1) what will be the slope at that point for both equations combined.

Question

1. The problem is the slope could be tangent to the f(x) so the slope would be 2.0001 but when its tangent to g(x) the slope is 3.0001.. so what would be the slope combined at that point for both functions.

Please give in fractions(answer) and ive just started to learn calculus....

(Im 14)

Answer 1

Your problem is that you have not clearly defined what you want.

The slope of f(x) at (1,1) is exactly 2; no 2.0001 about it!

And similarly the slope of g(x) at (1,1) is 3.

Now what do you mean by the "combined" slope?

The slope of h(x) = f(x)+g(x) is 5.

What you need to do is clarify what you mean by "combined".