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Well, honey, a point of discontinuity is not the same as a critical point in calculus. A critical point is where the derivative is either zero or undefined, while a point of discontinuity is where a function is not continuous. So, in short, they may both be important in their own ways, but they're not the same thing.
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Coachy=x+3/[(x-4)(x+3)] Definition: a critical number of a function f is a number c in the domain of f such that f'( c) = 0 or f'(c) doesn't exist. Since we have a rational function, the domain is all real numbers except the numbers that make the denominator zero. Therefore, x cannot be -3 and 4. There is a hole on the graph of the function at x = -3, and x = 4 is a vertical asymptote. Simplify first, then take the derivative of y. y = (x + 3)/[(x - 4)(x + 3)] = 1/(x - 4) y' = [1/(x - 4)]' use the quotient rule y' = [(x - 4)(0) - 1(1)]/(x - 4)^2 = -1/(x - 4)^2. Since the numerator is a constant, then y' is never zero, so there is not a critical point.
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What is function which is has irremovable discontinuity at x-2 removable discontinuity at x2 and continuous at other points?
"Removable discontinuity" means the function is not defined at that point (it has a "hole"), but by changing the function definition at that single point, defining it to be certain value, it becomes continuous. "Irremovable discontinuity" means the function makes a sudden jump at that point. There are infinitely many functions like that; for example, you can set the function to be: f(x) is undefined at x = -2 f(x) = 0 for x < 2 (except for x = -2) f(x) = 1 for x > 2
What is unremovable discontinuity?
If you have a discontinuity and you can cancel factors in the numerator and the denominator, then it is removable. If you can't cancel those factors to get rid of the discontinuity it is nonremovable. Here is an example that shows both kinds. f(x) = (x - 2)(x + 3) /[(x - 2) (x - 4) There is a discontinuity at x=2 but we can cancel out(x-2) from the top and bottom. That makes it removable. However, at x=4 there also a discontinuity and there is no way to remove that one.
What is the difference between a critical point and control point?
A Control Point or "CP" is any step in the flow of food where a physical, chemical or biological hazard can be controlled. Where as A Critical Control Point or "CCP" is the last step where you can intervene to prevent, eliminate or reduce a hazard to an acceptable limit.
What did the asymptote say to the removable discontinuity?
Don't hand that holier than thou line to me
What is the name for values of an independent variable for a function that make its derivative equal to 0 or not defined but are not within the domain of the original function?
That sounds a lot like a critical point to me.
