Use the mean value theorem to determine the value of c, given that f(x) = cos 5x. I got f(x)=cos 9.96. Pls check
To use the mean value theorem to determine the value of c, we need to find the derivative of the function f(x) and evaluate it at a specific point.
First, let's find the derivative of f(x) = cos 5x. The derivative of cos x is -sin x, and by using the chain rule, the derivative of cos 5x is -5sin 5x.
Next, we apply the mean value theorem, which states that if a function f(x) is continuous over an interval [a, b] and differentiable over the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).
In our case, we need to find a point c such that f'(c) = (f(b) - f(a)) / (b - a), where a and b are the endpoints of the given interval.
You mentioned that you got f(x) = cos 9.96. However, it's essential to know the interval [a, b] within which we want to find the value of c.
Please provide the interval [a, b] within which you would like to find the value of c, and I will help you further.