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Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative.
If the position of an object is specified by s(t) we know that the velocity is first derivative of the position.
v (t ) = s′ (t )
First derivative of any velocity is the acceleration of object; however since it is the first derivative of the position function we can also think of the acceleration as the second derivative of the position function.
a (t ) = v′ (t ) = s′′ (t )
Alternate Notation : There is couple of alternate notation for higher order derivatives. Recall as well that there was a fractional notation for the first derivative.
f ′ ( x ) = df /dx
We should extend this to higher order derivatives.
f ′′ ( x )= d 2 y / dx f ′′′ ( x ) = d 3 y/ dx etc.
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Example: A 16 lb object stretches a spring 8/9 ft by itself. Here is no damping as well as no external forces acting on the system. The spring is firstly displaced 6 inches upward
Now let's move onto the revenue & profit functions. Demand function or the price function Firstly, let's assume that the price which some item can be sold at if there is
(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1
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Jack and his mother paid $11.50 for tickets to the movies, and adults tickets cost $4.50 more than a child ticket what was the cost of each ticket?
Find the magnitude of the following vectors: 5i+7j
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Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans: Sum of all natural numbers in first 1000 integers which ar
The subsequent topic that we require to take a look at is the determinant of a matrix. The determinant is in fact a function that gets a square matrix and converts this in a number
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