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

In summary, a student needs help proving that a given function is not differentiable at x=0 and solving a problem involving a collapsing ladder. They are advised to set up an equation relating the height and length of the triangle formed by the ladder, wall, and floor, and use the given rate of change of the ladder's length to find the rate of change of its height. This conversation should have been posted in a calculus or homework help forum and the student is encouraged to improve their question formatting.
  • #1
lilac_lily
1
0
Hi I am 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?
 
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  • #2
lim f(x) x->0- doesn't equal lim f(x) x->0+

2 needs more info to solve i believe
 
  • #3
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
For the func.
f(x) = { 0 x < or/and = 0
2x +1 x > 0
That's barely comprehensible.

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

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.


-------------------------------------------------------

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?
 

1. Why is it important to prove that a function is not differentiable at x=0?

Proving that a function is not differentiable at a specific point can help identify potential issues or limitations with the function, and can provide insight into its behavior and properties.

2. What does it mean for a function to be not differentiable at x=0?

A function is not differentiable at a point if it does not have a well-defined slope at that point. This means that the function is not smooth and has a sharp corner, cusp, or vertical tangent at x=0.

3. How can I prove that a function is not differentiable at x=0?

To prove that a function is not differentiable at a point, you can use the definition of differentiability and show that the limit of the function's difference quotient does not exist at x=0. You can also look for discontinuities or non-differentiable points in the derivative of the function.

4. What are some common examples of functions that are not differentiable at x=0?

Some common examples of functions that are not differentiable at x=0 include absolute value functions, piecewise-defined functions with a discontinuity at x=0, and functions with a corner or cusp at x=0.

5. Can a function be not differentiable at x=0 but still be continuous at that point?

Yes, a function can be not differentiable at x=0 but still be continuous at that point. This means that the function does not have a well-defined slope at x=0, but it is still a continuous function and has no gaps or breaks at x=0.

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