Solving Questions on f(x) = x^2 + x and x/|x| at x=0

[BrendanM]

I kinda have a question and an answer check... well here's my check.

Let f(x) = x^2 + x. For any readl number a, let Ty be the y-intrecept of the tangent line to f(a), let Nx and Ny be, respectivly, the x-intercept and y-intercepts of the normal line to f(a). SHow that a = 0 is the only value for which the area of the triangle (0,Ny),(0,0),(Nx,0) is equal to the area of triangle (0,Ty),(0,0),(Nx,0).

to attack this problem i decided since the triangles both have side (0,0),(Nx,0) in common i could just find the equations of the tangent and normal line, find the intercepts of the tangent and normal and then set them equal in magnitude. i ended up with a^2 = a/(2a +1) + a^2 + a
when i solve i get x = 0, x=-1
it seems to work out when i plot the graphs for x = -1...
but in my question it says show that a = 0 is the only possible value, am i drawing it wrong or is my prof missing something? ty

question #2...

this should be an easy question...

f(x) = x/|x| at x = 0;

the derivative do not exist, explain why. There is a skip ?

Can the definitions be modified(slightly) so that the derviative does exist at this point, if so calc the derivative. if no explain why. i need help on this question :|

 

[arildno]

Question 2:
Draw the function on a piece of paper, and you'll see.

 

[BrendanM]

If anyone can help I am in major need :|

 

[HallsofIvy]

If anyone can help I am in major need :|

A function has to be continuous before it can be differentiable!

 

[BrendanM]

yah felt kinda silly by asking for help on #2, well for anyone who was wondering...for #1 my prof was wrong. He said he made a mistake after i confronted him about the two values.. Oh well sounds good. ty everyone that helped

 

[arildno]

Isn't it great when showing your prof. that he also makes mistakes..