Question

Of the infinitely many lines that are tangent to the curve y = −3 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

Answer 1

Here is my first stab at this - haven't got time to complete it now:

The slope of the curve is the first derivative

Use the product rule to get an expression for the slope (= d/dx(-3sinx))

Now - for a maximum value the derivative of THAT value= 0

So make a second derivative and set it to 0

Now you have an expression f(x) = 0

Newtons method entails an iterative approach - first make a 'guess' at the answer (X0) then repeat the Newtons method:

X1 = X0 - f(X0)/f'(X0)

Repeat until there is no change in the answer for six decimal places.

Answer 2

Thank you! I got it. I was missing the final step after finding where it doesn't change then I needed to put it in to the f'(x) and solve.