Question

We have two functions f(x) = |sin(x)| and g(x) = cos(x). What is the value of the slope of the line that passes through all the minima of the function h(x) = f(x) * g(x)?

Answer 1

To find the value of the slope of the line that passes through all the minima of the function h(x) = f(x) * g(x), we need to find the minima of the given function and then determine the slope of the line passing through those points.

Step-by-step explanation:

To find the value of the slope of the line that passes through all the minima of the function h(x) = f(x) * g(x), we need to find the minima of the given function and then determine the slope of the line passing through those points. First, let's find the minima of h(x) by finding the critical points where the derivative of h(x) is equal to zero.

The derivative of h(x) can be found using the product rule: h'(x) = f'(x)g(x) + f(x)g'(x). We have the functions f(x) = |sin(x)| and g(x) = cos(x), so f'(x) = cos(x) and g'(x) = -sin(x).

Now, we can find the critical points of h(x) by setting h'(x) = 0 and solving for x. Once we have the x-values of the minima, we can find the y-values using the function h(x). Finally, we can find the slope of the line passing through these minima using the formula slope = (change in y) / (change in x).