Chinkee Tan's birth name is Ferdinand Tan.
Yce Tan's birth name is Rycelonia Tan.
Teck Tan's birth name is Tan Chor Teck.
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Mika Tan :)
Weistrass function is continuous everywhere but not differentiable everywhere
No.
It is; everywhere except at x = 0
A cubic function is a smooth function (differentiable everywhere). It has no vertices anywhere.
Wherever a function is differentiable, it must also be continuous. The opposite is not true, however. For example, the absolute value function, f(x) =|x|, is not differentiable at x=0 even though it is continuous everywhere.
An intuitive answer (NOTE: this is far from precise!) A function is continuous if you can trace its graph without lifting your pencil from the page. If, additionally, it is smooth everywhere without any jagged edges or abrupt corners, then it is differentiable. It is not possible for a function to be differentiable but not continuous. On the other hand, plenty of functions are continuous without being differentiable.
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The signum function, also known as the sign function, is not differentiable at zero. This is because the derivative of the signum function is not defined at zero due to a sharp corner or discontinuity at that point. In mathematical terms, the signum function has a derivative of zero for all values except at zero, where it is undefined. Therefore, the signum function is not differentiable at zero.
Definition: A function f is differentiable at a if f'(a) exists. it is differentiable on an open interval (a, b) [or (a, ∞) or (-∞, a) or (-∞, ∞)]if it is differentiable at every number in the interval.Example: Where is the function f(x) = |x| differentiable?Answer:1. f is differentiable for any x > 0 and x < 0.2. f is not differentiable at x = 0.That's mean that the curve y = |x| has not a tangent at (0, 0).Thus, both continiuty and differentiability are desirable properties for a function to have. These properties are related.Theorem: If f is differentiable at a, then f is continuous at a.The converse theorem is false, that is, there are functions that are continuous but not differentiable. (As we saw at the example above. f(x) = |x| is contionuous at 0, but is not differentiable at 0).The three ways for f not to be differentiable at aare:a) if the graph of a function f has a "corner" or a "kink" in it,b) a discontinuity,c) a vertical tangent
Well, firstly, the derivative of a function simply refers to slope. Usually we say that the function is not differentiable at a point.Say you have a function such as this:f(x)=|x|Another way to represent that would be as a piece-wise function:g(x) = { -x for x= 0The problem arises at the specific point x=0. If you look at the slope--the change in the function--from the left and right of x, you notice that it is different, negative 1 and positive 1. So, we can say that the function is not differentiable at x=0 because of that sudden change.There are however, a few functions that are nowhere differentiable. One example is the Weirstrass function. The even more ironic thing about this function is that it is continuous everywhere! Since this function is not differentiable anywhere, many might call it a non-differentiable function.There are absolutely other examples.
The existence of a derivative function at a given point depends on the behavior of the original function at that point. A derivative exists at a point if the function is continuous and has a defined slope (i.e., is differentiable) at that point. However, there are functions that are not differentiable at certain points—such as those with sharp corners, vertical tangents, or discontinuities—meaning the derivative does not exist for all values of ( x ). Thus, while many functions are differentiable everywhere, not all functions possess derivatives across their entire domain.
If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.