More generally, the graphs of two functions f(x) and g(x) are
tangent at x=a if f(a) = g(a) and f'(a) = g'(a). For example,
the functions and g(x) = x are tangent at x=0,
but the functions and q(x) = x+1 are not tangent at
x=0, even though they have the same slope, because p(0) = 0 and
q(0) = 1 so the graphs of p and q don't intersect at x=0.
Suppose that and . Determine if the
following statements are true or not.
- is tangent to 1/f(x) at x=-1.
- is tangent to f(x)g(x) at x=1.
- is tangent to f(x)/g(x) at x=1.
- is tangent to at .