Examples of using Second derivative in English and their translations into Arabic
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Colloquial
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Political
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Ecclesiastic
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Ecclesiastic
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Computer
Another example of a non-linear equation is if I wrote y times the second derivative of y with respect to x is equal to sine of x.
Now if the second derivative equals 0,
Well, what that means is that the second derivative, which is the slope of the slope,
That means that A times the second derivative of h plus B times h prime plus C times h is equal to 0.
So what we have to do, is see whether the second derivative is positive or negative on either side of 2/3.
So that means that when x is greater than 2/3, that tells us that the second derivative is positive.
So there's no way that the second derivative can ever be 0, and thus we have proved that a quadratic has no point of inflection. see you in the next video.
So in that case as well, we will have a positive times a negative divided by a positive, so then our second derivative is going to be negative.
So what does that tell us, given that that is a positive constant Number That tells us that at any value of a, the second derivative is positive.
So when the second derivative is zero, it might be an inflection point,
you don't have a y times the second derivative of y.
So let's say I have this differential equation, the second derivative of y, with respect to x, plus 5 times the first derivative of y,
So let's say that I have the second derivative of my function y plus 4 times my function y is equal to sine of t minus the unit step function 0 up until 2 pi of t times sine of t minus 2 pi.
Well, we can take the second derivative of this function, see what the second derivative is at x equals 4, and then see if we're concave upwards or concave downwards.
So I have this equation here, this initial value problem, where it says that the second derivative of y plus 2 times the first derivative of y, plus 2 times y, is equal to sine of alpha t.
So we get the second derivative of g, which is our guess solution, is equal to the second derivative of v prime,
Now if this equation were-- if I rewrote it as x squared d, the second derivative of y with respect to x squared, is equal to sine of x, and let's say I were to square this.
So in the last video-- it was either the last one or the previous one-- I showed you that the Laplace Transform of the second derivative of y is equal to s squared times the.
The uses of the first and second derivative to determine the intervals of increase and decrease of a function, the maximum and minimum points, the interval(s) of concavity and points of inflections are discussed.
And the second derivative of y1 is equal to-- we will just take the derivative of this, and that's just equal to