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Is it always true that for any polynomial px if x is a zero of the derivative then x px is a maximum or minimum value of px?
No. The important decider is the second derivative of the polynomial (the gradient of the gradient of the polynomial) at the zero of the first derivative: If less than zero, then the point is a maximum If more than zero, then the point in a minimum If equal to zero, then the point is a point of inflection. Consider the polynomial f(x) = x3, then f'(x) = 3x2 f'(0) = 0 -> x = 0 could be a maximum, minimum or point of inflection. f''(x) = 6x f''(0) = 0 -> x = 0 is a point of inflection Points of inflection do not necessarily have a zero gradient, unlike maxima and minima which must. Points of inflection are the zeros of the second derivative of the polynomial.
Relationship between Integration and differentiation?
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
When using the derivative classification concept of compilation you must place?
True
What does it mean when the line is curved on a graph?
it is infinite and is a parabolaIts first derivative is non-zero* * * * *That is not a proper answer. All that it means is that the relationship between the two variables in question (x and y) is some nonlinear continuous function.It need not be infinite - a graph can be a circle: that is curved but is certainly not infinite. It could also be an ellipse, a hyperbola, a polynomial of any degree other than 1, an exponential or logarithmic curve, a trigonometric curve, or any combination of the above - as well as other curves.The point about the first derivative is true, but that also applies to any straight line that is not horizontal.Actually the first derivative can be zero at specific point(s), but this is specifically true whereas a non-zero value is generally true.
What must be true about the coordinates of any point that lies in the third quadrant?
Both coordinates are negative in this case.
Is it always true that for any polynomial px if x is a zero of the derivative then x px is a maximum or minimum value of px?
No. The important decider is the second derivative of the polynomial (the gradient of the gradient of the polynomial) at the zero of the first derivative: If less than zero, then the point is a maximum If more than zero, then the point in a minimum If equal to zero, then the point is a point of inflection. Consider the polynomial f(x) = x3, then f'(x) = 3x2 f'(0) = 0 -> x = 0 could be a maximum, minimum or point of inflection. f''(x) = 6x f''(0) = 0 -> x = 0 is a point of inflection Points of inflection do not necessarily have a zero gradient, unlike maxima and minima which must. Points of inflection are the zeros of the second derivative of the polynomial.
Aniline dyes are derived from benzene a coal tar derivative true or false?
True. Aniline dyes are derived from benzene, which is a coal tar derivative.
What are a set of points equidistant from a given point?
Congruent. If the two points are an equal distance from a third point, then those two points are congruent to each other, in respect to the third point. This is a true statement, but it may not be what the question is looking for.
Relationship between Integration and differentiation?
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
What true statement concerning derivative classification?
Derivative classifiers are responsible for analyzing and evaluating information to identify elements that require classification.
When using the derivative classification concept of compilation you must place?
True
When using the derivative classification concept of compilation you must place a?
True
Select the true statement concerning derivative classification?
Derivative classifiers are responsible for analyzing and evaluating information to identify elements that require classification.
Select true statement concerning derivative classification?
Derivative classifiers are responsible for analyzing and evaluating information to identify elements that require classification.
Select the true statement concering derivative classification?
derivative classifiers are responsible for analyzing and evaluating information to identify elements that require classification
Why the derivative is set equal to zero?
The first derivative is set to zero to find the critical points of the function. A critical point can be a minimum, maximum, or a saddle point. There's a reason for this. Suppose a differentiable function f:R->R has a maximum at x=a. Then the function goes down to the right of a, which means f'(a)
Is an important responsibility of the derivative classifier to observe and respect the original classification authority and to use only authorized sources to determine derivative classification?
true
