Explanation The derivative of the function is basically the method to determine the rate of change of one value with respect to some other variable. Second derivative is the derivative of the derivative of a function. For example, Consider a function, f ( x ) = sin 2 x Derivative of the function is f ′ ( x ) = 2 cos 2 x . Then second derivative of the function is, f ″ ( x ) = − 4 sin 2 x f ″ ( x ) = − 4 f ( x ) Consider another example, f ( x ) = cos 2 x Derivative of the function is f ′ ( x ) = − 2 sin 2 x

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Chapter 9.2, Problem 76E

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The two examples of a function f(x) with the property that f″(x)=−4f(x).

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Chapter 9.2, Problem 75E

Chapter 9.2, Problem 77E

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Chapter 9 Solutions

Applied Calculus, Loose-leaf Version

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The two examples of a function f ( x ) with the property that f ″ ( x ) = − 4 f ( x ) .

Solution Summary: The author explains that the derivative of a function is basically the method to determine the rate of change of one value with respect to some other variable.

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The two examples of a function f(x) with the property that f″(x)=−4f(x).

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Chapter 9 Solutions