How to Find the Second Derivative with Given Equation at a Specific Point?

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Thread starter karush
Start date Nov 7, 2019
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Derivative Second derivative Value

In summary, The second derivative is the rate of change of the first derivative. It is important because it can tell us the rate of change of the rate of change of a function, which can provide valuable information about the behavior of the function. The second derivative is calculated by taking the derivative of the first derivative and can also be calculated by using the limit definition of the derivative. A positive second derivative indicates that the slope of the graph is increasing, while a negative second derivative indicates that the slope of the graph is decreasing. These can indicate whether the function is concave up or concave down and can provide information about the increasing or decreasing rate of the function. In real-world applications, the second derivative can be used to find maximum or minimum points

Nov 7, 2019

karush

Gold Member

MHB

If $(x+2y)\cdot \dfrac{dy}{dx}=2x-y$ what is the value of $\dfrac{d^2y}{dx^2}$ at the point (3,0)?
ok not sure of the next step but
$\dfrac{dy}{dx}=\dfrac{2x-y}{x+2y}$

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Nov 7, 2019

Greg

Gold Member

MHB

Re: 231 value of second dirivative

See https://mathhelpboards.com/calculus-10/297-ap-calculus-exam-2nd-derivative-26690.html.

What is the second derivative?

The second derivative is a mathematical concept that represents the rate of change of the first derivative. It is the derivative of the derivative, or the rate of change of the rate of change.

Why is the second derivative important?

The second derivative is important because it can provide information about the shape and behavior of a function. It can be used to determine the concavity of a curve, identify points of inflection, and find the maximum and minimum values of a function.

How is the second derivative calculated?

The second derivative is calculated by taking the derivative of the first derivative. This can be done using the power rule, product rule, quotient rule, or chain rule, depending on the form of the function.

What is the relationship between the second derivative and the graph of a function?

The second derivative can help determine the shape of a function's graph. A positive second derivative indicates a concave up curve, while a negative second derivative indicates a concave down curve. Points of inflection occur when the second derivative changes sign.

How is the second derivative used in real-world applications?

The second derivative is used in various fields, such as physics, engineering, and economics, to analyze and model real-world phenomena. It can be used to optimize functions, predict the behavior of systems, and solve problems involving rates of change.