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Use Newton's method to find the absolute maximum value of the function $ f(x) = x\cos x $, $ 0 \leqslant 0 \leqslant \pi $, correct to six decimal places.

$\approx 0.561096$ is the absolute maximum value of $f$

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question 36. We start with of X equals X, come sign of X and they give us the rail and that would give us and cry. Um, refuse our product rule of your f of the RG prime times G plus g prime we give us Come sign. It's frying, June. But cheap crime frying the derivative of coastline is negative. Sign time? No, but my experts So I use that and why my estimates around next equals quite nine. So now I'm gonna use my gene rack. My Jew equals co signed X minus x sign of X Oh, my g prime is gonna equal co sign. I have negative sign of X minus the nephews My product. Cool sign of X minus co sign of X Have been combined. My light terms. Prime of X. Negative, too Sign and eggs minus goes. I haven't x there. So now Newton says I'm gonna use thanks minus G over Ji Prime to get my approximation using X is approximately 0.9. That gives me except one That's exit one exit too. Wait 86 The row 33 over Pics of three then Hey, we a b ro 334 which is the same thing I get for except for. And when I put that into my function, my absolute minimum become 1860 334 My six won the round. I'm six.

University of Houston