Recent content by TheIdealist

Is this correct? \intf(x) - f'(r)(x-r)+f(r). I solved for the tangent line by solving for y-f(r)=f'(r)(x-r). This is just the generic point slope formula. I can't find a way to rewrite x in terms of a and r in the integral.

Ok, after integrating the function f(x) and the tangent line y= f'(r)(x-r)+f(r) on [0,a], I got F(a)-F(0)-[f'(r)a^2]/2 - f'(r)ra + f(r)a. I got this from integrating both the function and the tangent line and setting up a difference between them. Is this correct? If it is, how would I minimize...

Thanks for replying! I think I was able to solve for the area for e^x. I integrated f(x)= e^x from 0 to a and got F(x)= e^a-1. I then solved for the tangent line. I think it is f(x)- e^r=(e^r)(x-r). I then have to integrate the difference right? After integrating the difference from 0 to a, I...

Homework Statement Suppose C:y=f(x) with f a twice-differentiable function such that f''(x)> 0 for each x on the closed interval [0,a] where a is a positive constant. Suppose T is the tangent line to C at a point P= (r,f(r)) on C where r is in the open interval (0,a). Let A be the area of the...