0
What else can I help you with?
How does the second deriative work i understand the first deriative but i dont really understand how the second deriative gives you the answer of a whether a stationary point is a minimum or maximum?
The first deriviative is the slope of the function. Your understanding is somewhat correct, in that when the first deriviative is zero, the function is at a minimum or a maximum. (Or an inflection point)Take this one step further. The second deriviative is the slope of the first deriviative. Take a moment to understand what this means...If the slope of a function is positive, then the value of the function is increasing. If the slope of a function is negative, then the value of the function is decreasing. Last, if the slope of a function is zero, then the value of the function is not changing - this is why a value of zero for the first deriviative means you are at a maximum or a minimum. (Or an inflection point - more on that later.)OK. If the slope of the first deriviative, i.e. the slope of the slope of the initial function is positive, that means the first derviative is increasing, which means the function is accelerating upward.Make sure you understand the geometric implications here - it is critical towards understanding the problem. If the first deriviative is zero and the second deriviation is positive, then you are sitting at a minimum. If the first deriviative is zero and the second deriviative is negative, then you are sitting at a maximum.Now for the inflection point... If the first deriviative is zero and the second deriviative is zero, you are not at a maximum or a minimum - you are at an inflection point - a point where the slope goes to zero - but you don't know if it is going to change to the same direction it is going.For example, look at y = x3. The first deriviative y' = 3x2, which is zero at x=0, and the second deriviative y'' = 6x, which is also zero at x=0. The point x=0 is an inflection point, not a maximum or minimum, and you know that because the second deriviative is also zero.You can take this to any level you want, such as looking at the third deriviative. The original question was how to identifiy if a point where the first deriviative is zero represents a maximum or a minimum.
What is the derivative of 0?
If you mean "what is the deriviative of f(x) = 0?", the answer is 0. (zero) The deriviative of any constant is zero.
What is the general formula for nth derivative of f equals sinx?
The first deriviative of sin(x) is cos(x), which is also sin(x + pi/2). The general formula, then for the nth deriviative of sin(x) is sin(x + n pi/2).
What is the anti-deriviative of 14dt?
∫14dt = 14t + c(where c is a constant)
What happen sinx when you find its derivative?
The deriviative of sine(x) is cosine(x).
The expression x to the power of 2 - 2mx has a minimum value as x varies Find the minimum value of x to the power of 2 - 2mx and Give your answer in terms of m?
If this is a homework question, please consider answering it on your own first, otherwise the value of the homework assignment, i.e. to reinforce the lesson, will be lost to you.The minimum or maximum of a function y = f(x) can be found when the deriviative dy/dx f(x), or slope, is zero. In the case of a polynomial of degree two, which this question is, there is only one point where the deriviative is zero. In the general case of a polynomial of degree three or higher, however, any point where the slope is zero might only be a local minimum or maximum, so care must be taken. Also, you must always consider the second deriviative, in order to verify if that point is a minumum or a maximum.The first deriviative of y = x2 - 2mx is 2x - 2m. (Remember, m is constant)By simple algebra, the solution of 2x - 2m = 0 is x = m.To determine if this is a minimum or a maximum, take the second deriviative.The second deriviative of y = x2 - 2mx is the first deriviative of y = 2x - 2m, which is 2.Since 2 is always positive, the slope is always increasing, so the point x = m is a minimum.
How do you find points of inflection in calculus?
Points of inflection on curves are where the curvature changes sign, such as when the second deriviative changes sign
When using deriviative classificaiton concept of compilation you must place a clearly worded explanation of the basis for classification by compilation on the face of the document or include it in the?
True
Function of y equals mx plus c?
The equation y = mx + c, is the equation of a line in slope-intercept form. The m term is the slope or first order deriviative (dy/dx) of the line, and the c term is the y-axis intercept.
How do you differentiate sin squared x plus cos squared x?
The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x
How differentiation of x equals 1?
The deriviative of f(x) = x is 1 because the slope of the function f(x) = x is 1. Recall the slope-intercept form of a line. The equation f(x) = x can also be stated as y = mx+b, where m is 1 and b is 0. The slope is m, or 1, and the deriviative of f(x) is the slope of f(x), which is m or 1, in this case.
Why is e a natural logarithm?
The number e, 2.718281828..., was chosen as the "natural" base for logarithms and powers because it is the only number where the deriviative of e to the x is x... d/dy ex = x
