Asked by TayB

Of the infinitely many lines that are tangent to the curve
y = −4 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.

Answers

Answered by Steve
A quick look at the graph shows that the point we want will be somewhere in the interval [pi,2pi].

The line through (0,0) and (x,-4sinx) is

y = -4sinx/x

we also know that at any point x, the slope is

y' = -4cos(x)

So, we need

-4sin(x)/x = -4cos(x)
tanx = x

So, let f(x) = tanx-x

Pick x = 4.7 (near 3pi/2, which is an asymptote) as the initial guess, and apply Newton's method to that. I get x=4.493
Answered by TayB
That's not correct Steve that's not to six decimal places like the problem says
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