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Does anyone know how to do #12 and #14? | Does anyone know how to do #12 and #14? | ||
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| + | 12) So to show that x* is an absolute minimum we can define a new function h(x) = cosx-x^2. [h(0)>0 and h(pi/2)<0 so LRT applies] | ||
| + | So we know there exists an x* in I such that h(x*)=0 and cos(x*)=(x*)^2 | ||
| + | So we basically use this identity, along with the fact that x^2 is increasing on I and cosx is decreasing on I. | ||
| + | Ill show how to do the case for x>x*. At any x>x*, x^2>cosx so your f(x) will be x^2 because it is the larger value. so f(x)=x^2> x*^2=f(x*) | ||
| + | The same applies when x<x* just with cosx>cos(x*) J. Gars | ||
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| + | |||
| + | And #14 is pretty much just using the hint provided in the book where | ||
| + | Limx->x*(B-f(x)) = B-Limx->x* f(x)>0....then a neighborhood where b-f(x)>0 => f(x)<B. Could be wrong on this who knows. J.Gars | ||
| + | Some help with 5.3.2 would also be appreciated I can't seem to figure it out. | ||
That would be lovely.. I second this question. | That would be lovely.. I second this question. | ||
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Can anyone formulate 5.3.2 and 5.3.4? I am having difficulties with these problems.
I'm not sure what to do for 5.3.2 either.
For #4 your can let p(x)=a(x)^n where n is odd and a is a coefficient.
Then by 4.3.16 limp(x) as x-inf =inf and lim(p(x)) as x= -inf = -inf
thus there exist x, such that p(x)>0 and x such that p(x)<0 then you can use the Root thereom.
M. Niekamp
Does anyone know how to do #12 and #14?
12) So to show that x* is an absolute minimum we can define a new function h(x) = cosx-x^2. [h(0)>0 and h(pi/2)<0 so LRT applies] So we know there exists an x* in I such that h(x*)=0 and cos(x*)=(x*)^2 So we basically use this identity, along with the fact that x^2 is increasing on I and cosx is decreasing on I. Ill show how to do the case for x>x*. At any x>x*, x^2>cosx so your f(x) will be x^2 because it is the larger value. so f(x)=x^2> x*^2=f(x*) The same applies when x<x* just with cosx>cos(x*) J. Gars
And #14 is pretty much just using the hint provided in the book where
Limx->x*(B-f(x)) = B-Limx->x* f(x)>0....then a neighborhood where b-f(x)>0 => f(x)<B. Could be wrong on this who knows. J.Gars
Some help with 5.3.2 would also be appreciated I can't seem to figure it out.
That would be lovely.. I second this question.
