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.
yes...
No, a non-continuous function cannot be differentiable at the points of discontinuity. Differentiability requires the existence of a well-defined tangent line at a point, which necessitates continuity at that point. However, a function can be differentiable on intervals where it is continuous, even if it has discontinuities elsewhere.
Hair colour is continuous because there is a continual range of values when it comes to hair colour
The function ( R(z) ) is differentiable in regions where it is complex differentiable, meaning it satisfies the Cauchy-Riemann equations. Typically, this applies to regions in the complex plane where the function is continuous and its partial derivatives exist. If ( R(z) ) is expressed in terms of real variables ( x ) and ( y ) (where ( z = x + iy )), it is differentiable at points where these conditions hold true. Thus, the specific answer depends on the form of ( R(z) ).
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.
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
discontinuous
No.
Here are some: odd, even; periodic, aperiodic; algebraic, rational, trigonometric, exponential, logarithmic, inverse; monotonic, monotonic increasing, monotonic decreasing, real, complex; discontinuous, discrete, continuous, differentiable; circular, hyperbolic; invertible.
Weistrass function is continuous everywhere but not differentiable everywhere
Natural eye colour is discontinuous. :) !
graph gx is the reflection of graph fx and then transformed 1 unit down
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
Discontinuous innovation is innovation that is divorced from prior common knowledge.
The tangent function, ( \tan(x) ), is not differentiable everywhere. It is differentiable wherever it is defined, which excludes points where the function has vertical asymptotes, specifically at ( x = \frac{\pi}{2} + k\pi ) for any integer ( k ). At these points, the function approaches infinity, leading to a discontinuity in its derivative. Thus, while ( \tan(x) ) is smooth and differentiable in its domain, it is not differentiable at the points where it is undefined.
yes a discontinuous function can be developed in a fourier series
Discontinuous. There's no middle ground, someone either has it or doesn't.