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what does it mean when f(x) is differentiable along an interval?
it means that f is continuous along that domain. In other words, the curve f is smooth and does not break at any point along the interval.
what does it mean when f(x) is differentiable at a point c?
It means that f is continuous above the domain given by the interval that is an infinitesimally small distance from c. In other words the curve, f(x), is smooth and does not break along the differentially small interval given by c and at all of the values unimaginably close to c.
what does it mean when the derivative of f(x) at c equals 2?
It means that the instantaneous rate of change (slope) of f(x) at that point is equal to 2.
what does it mean when the derivative of f(x) everywhere along an interval equals 2?
It means that every single point along that interval has the same slope of 2. In other words, that interval yields a line with a slope of 2.
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When was function not having a derivative at a point?
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
Is function f of x equal to modulus x differentiable?
It is; everywhere except at x = 0
If f x equals x-x plus2 what does f-3 equal?
-1
How many f orbitals have the value n equals 2?
2
How do you differentiate a fraction with x as a numerator?
Suppose you wish to differentiate x/f(x) where f(x) is a differentiable function of x, and writing f for f(x) and f'(x) for the derivative of f(x), d/dx (x/f) = [f - x*f']/(f2)
