Slopes of tangent lines to curves at pt where lines furthest

[Sophia27]

Two curves y=f(x) and y = g(x) start and end on the interval [a,b]. the function f(x) increasing but has a concave down shape and g(x) is increasing but has a convave up shape. Both functions are differentiable and "c"=the point where the curves are the farthest apart. What is special about the tangent lines to the curves at point c? Explain.

I don't know how or if i need to explain this in mathematical terms but I suspect the tangent lines to the curves at point c have equal slopes. I know this would be alot easier if i could show the graph.

*point c is between a and b

 

[mmm4444bot]

Re: Slope of the tangent lines between 2 curves

... What is special about the tangent lines to the curves at point c? Explain.

I don't know ... [whether or not] i need to explain this in mathematical terms ... My opinion is that using mathematical terms is generally a good idea when providing requested explanations in a math exercise.

... but I suspect the tangent lines to the curves at point c have equal slopes ... Are you able to explain why you suspect this?

 

[Sophia27]

Re: Slope of the tangent lines between 2 curves

Yea I figured the problem out. I realized the two curves share the same secant line AB so therefore my the mean value theorem it states that there is at least one point c where the tangent line is parallel to the secant line.