You are dealing with functions that accept one variable. Multivariable calculus deals with functions that accept multiple variables. For example, $f(x,y) = x^2+y^2$. Try that out in wolframalpha. It produces a graph in three-dimensional space. Tangents in three-dimensional space can be multi-dimensional. Instead of a tangent line, you start talking about tangent planes (if you are looking at a two-dimensional object in three-dimensional space) or even tangent spaces (if you look at r-dimensional objects in n-dimensional space where $n>r$).