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All it means to take the second derivative is to take the derivative of a function twice.
For example, say you start with the function y=x2+2x
The first derivative would be 2x+2
But when you take the derivative the first derivative you get the second derivative which would be
2
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How do you find the slope of a tangent?
Take the derivative of the function.
What is the difference between nonlinear and linear functions?
Linear function:No variable appears in the function to any power other than 1.A periodic input produces no new frequencies in the output.The function's first derivative is a number; second derivative is zero.The graph of the function is a straight line.Non-linear function:A variable appears in the function to a power other than 1.A periodic function at the input produces new frequencies in the output.The function's first derivative is a function; second derivative is not zero.The graph of the function is not a straight line.
What is the Product rule for square roots?
the product rule is included in calculus part.Product Rule : Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functionsif you need more explanation, i want you to follow the related link that explains the concept clearly.
What is the derivative of e2x-1?
3
How do you know if a point is a maximum or a minimum?
Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.
What is the second derivative of a function's indefinite integral?
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
What is the geometrical meaning for second derivative?
The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.
How do you get the second derivative of potential energy?
To get the second derivative of potential energy, you first need to calculate the first derivative of potential energy with respect to the variable of interest. Then, you calculate the derivative of this expression. This second derivative gives you the rate of change of the slope of the potential energy curve, providing insight into the curvature of the potential energy surface.
If second derivative is 0 and third derivative is 0 What is true about that point?
If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.
How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
How do you find the maximum in a math problem?
It depends on the function whose maximum you are trying to find. If it is a well behaved function over the domain in question, you could differentiate it and set its derivative equal to 0. Solve the resulting equation for possible stationary points. Evaluate the second derivative at these points and, if that is negative, you have a maximum. If the second derivative is also 0, then you have to go to higher derivatives (if they exist). If the function is not differentiable, you may have a more difficult task at hand.
f(x)= â x2fâ˛â˛(x)=?
The function given is (f(x) = -x^2). The second derivative of a function, denoted as (fâ'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (fâ(x)) is (-2x). Taking the derivative of (fâ(x)) gives us the second derivative (fââ(x)), which is (-2). So, (fâ'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.
How do you find the slope of a tangent?
Take the derivative of the function.
Where the graph of a function equals the value zero?
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
What is the difference between nonlinear and linear functions?
Linear function:No variable appears in the function to any power other than 1.A periodic input produces no new frequencies in the output.The function's first derivative is a number; second derivative is zero.The graph of the function is a straight line.Non-linear function:A variable appears in the function to a power other than 1.A periodic function at the input produces new frequencies in the output.The function's first derivative is a function; second derivative is not zero.The graph of the function is not a straight line.
How do you integrate functions?
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
