# Prove that f(x) is not differentiable at x=0

1. Apr 21, 2004

### lilac_lily

Hi im a calc student in great need. If any1 can please help me thank u very much.

Here it is

For the func.
f(x) = { 0 x < or/and = 0
2x +1 x > 0
Proove that f(x) is not differentiable at x=0

Also
2. A two piece ladder leaning against a wall is collapsing at a rate of 2 ft/sec while the foot of the ladder remains a constant 5 ft from the wall. How fast is the ladder moving down the wall when the ladder is 13 ft long?

2. Apr 21, 2004

### cair0

lim f(x) x->0- doesnt equal lim f(x) x->0+

3. Apr 21, 2004

### gnome

Why is this in differential equations? Should be in calculus or homework help.

And if you're going to be posting questions here you should learn to do better than this
That's barely comprehensible.

I think this is what you mean:
$$f(x) = \left\{ \begin{array}{cc} 0 & for\; x <= 0\\ 2x + 1 & for\; x > 0 \end{array}$$

If so, in order for f(x) to be differentiable at x=0, the limit of the value of f(x) as x approaches 0 from the left must be equal to the limit of the value of f(x) as x approaches 0 from the right. To prove that f(x) is not differentiable at x=0, you have to show that these limits are not the same.

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For the other question, look at the triangle formed by the ladder, the wall and the floor. Set up an equation that relates the height (H) of this triangle to the length (L) of the ladder. You have been given dL/dt. You are asked to find dH/dt. Can you figure out what to do next?