Question

Use Newton's method to find the absolute maximum value of the function f(x) = 6x sin x, 0 ≤ x ≤ π correct to six decimal places.

Answer 1

My calculator froze when I typed in (pi/2)- [y1(pi/2)/y2(pi/2)] with y1= f(x) and y2= f'(x)

Answer 2

By differentiating f(x) with the Product Rule:
f'(x) = 6sin(x) + 6x*cos(x) = 0.

Then, setting f'(x) = 0 gives:
6sin(x) + 6x*cos(x) = 0 ==> tan(x) + x = 0.

Then, use Newton's Method to solve tan(x) + x = 0 on 0 <= x <= π. This solves to get x ≈ ?. Using the Second Derivative Test, you can show that this gives a maximum. Then you'll get the required maximum value .
hope it 'd be helpful

Answer 3

whoaa I learned this a completely different way!
So... i do the Second Derivative of f'(x) = 6sin(x) + 6x*cos(x)

which equals: f''(x) = 6cos(x) - [6x*sin(x) * 6cos(x)]
And find the maximum from there?

Answer 4

The first derivative test is to find the extreme points of f(x)

The second derivative test is to verify if those points will have a positive (minimum point) or negative (maximum point) concavity