Question:
Find the second order derivatives of the function
\(x^2+3x+2\)
Find the second order derivatives of the function
\(x^2+3x+2\)
\(x^2+3x+2\)
Updated On: Sep 24, 2023
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Solution and Explanation
The correct answer is 2
Let \(y=x^2+3x+2\)
Then,
\(\frac{dy}{dx}=\frac{d}{dx}(x^2)+\frac{d}{dx}(3x)+\frac{d}{dx}(2)=2x+3+0=2x+3\)
\(∴\frac{d^2y}{dx^2}=\frac{d}{dx}(2x+3)=\frac{d}{dx}(2x)+\frac{d}{dx}(3)=2+0=2\)
Let \(y=x^2+3x+2\)
Then,
\(\frac{dy}{dx}=\frac{d}{dx}(x^2)+\frac{d}{dx}(3x)+\frac{d}{dx}(2)=2x+3+0=2x+3\)
\(∴\frac{d^2y}{dx^2}=\frac{d}{dx}(2x+3)=\frac{d}{dx}(2x)+\frac{d}{dx}(3)=2+0=2\)
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Concepts Used:
Second-Order Derivative
The Second-Order Derivative is the derivative of the first-order derivative of the stated (given) function. For instance, acceleration is the second-order derivative of the distance covered with regard to time and tells us the rate of change of velocity.
As well as the first-order derivative tells us about the slope of the tangent line to the graph of the given function, the second-order derivative explains the shape of the graph and its concavity.
The second-order derivative is shown using \(f’’(x)\text{ or }\frac{d^2y}{dx^2}\).