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dimpledur
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Homework Statement
if f(x)=cos2x, how do we know that f^50 = f^2 ??
In the solution it states that because 50 = (12)(4) + 2, then f^50 = f^2.
What the??
High order derivatives refer to the derivatives of a function that have been taken multiple times. They represent the rate of change of the rate of change of the original function.
High order derivatives can be calculated using the same methods as regular derivatives, such as the power rule or the product rule. The only difference is that the derivative is taken multiple times, depending on the order.
High order derivatives can provide more detailed information about the behavior of a function, such as the curvature or inflection points. They are also important in fields such as physics and engineering, where higher order derivatives represent acceleration and other important quantities.
Taylor series is a mathematical tool used to approximate a function with an infinite series of derivatives. High order derivatives play a crucial role in determining the accuracy of this approximation, as the higher order terms are often what contribute to the error.
Yes, high order derivatives can be negative. This means that the function is decreasing at an increasing rate. For example, if the second derivative is negative, the function is concave down, and if the third derivative is negative, the function is concave down at an increasing rate.