Use Newton's method to find the absolute maximum value of the function f(x) = 5x cos(x), 0 ≤ x ≤ 𝜋,

Answer 1

To find the x value that generates the maximum value for this function apply the 1st (or 2nd) derivative test.

f'(x) = 5cosx - 5xsinx

When does that equal zero?

That is where Newton's method comes into play.

You might want to think of this 1st derivative as g(x) = 5 cos(x) - 5xsin(x)

Find g'(x) and apply Newton's Method with x₁ = π/2 (for example).

After applying Newton's Method you can use the 2nd derivative test to show that this is generating a maximum value for the original function, plug that value into the original to get the max value for "f" on the interval from 0 to π.