Calculate the instantaneous rate of change to the graph ofxexf x sin73)( at x = 0. Showyour work
Question
Calculate the instantaneous rate of change to the graph ofxexf x sin73)( at x = 0. Showyour work
Solution
The function given is f(x) = x + e^sin(73x).
The instantaneous rate of change at a point is given by the derivative of the function at that point.
First, we need to find the derivative of the function.
The derivative of x is 1.
The derivative of e^u, where u is a function of x, is e^u * u', where u' is the derivative of u.
In this case, u = sin(73x), so u' = 73cos(73x) by the chain rule.
Therefore, the derivative of e^sin(73x) is e^sin(73x) * 73cos(73x).
Adding these together, the derivative of the function f(x) is 1 + e^sin(73x) * 73cos(73x).
To find the instantaneous rate of change at x = 0, we substitute x = 0 into the derivative.
At x = 0, sin(73x) = 0 and cos(73x) = 1.
Therefore, the derivative at x = 0 is 1 + e^0 * 73 * 1 = 1 + 73 = 74.
So, the instantaneous rate of change to the graph of the function at x = 0 is 74.
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