# Thread: One more Calculus Problem

1. ## One more Calculus Problem

4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.

2. Forgot to put the graph here.

3. Originally Posted by Prophet
4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.
the vertical distance between the functions at any value of $x$ is given by $f(x) - g(x)$. define a new function, $h(x)$, to be this distance. thus we have:

$h(x) = f(x) - g(x)$

now we want to maximize $h$. so we find its derivative and set it equal to zero, thus we have:

$h'(x) = f'(x) - g'(x) = 0$

what can we say about $f'(x)$ and $g'(x)$? which are the slopes of the tangent lines of $f(x)$ and $g(x)$ respectively