Antiderivative graphing question - help

[Slimsta]

Homework Statement

http://img64.imageshack.us/img64/5430/80433637.jpg

Homework Equations

The Attempt at a Solution

for a, would it be local.max: x=7.7 and local.min: x=4.8 ?
and for b, abs.max: x=11 and abs.min: x=2 ?

im not sure if i did it right but looks like this isn't what the question wants me to do..

 

[Mark44]

The graph you show is f(x) = xsinx. The function you're investigating is $$g(x)~=~\int_0^x t sin(t)dt$$

How would you ordinarily go about find the local max or min of a function?

Have you learned about the Fundamental Theorem of Calculus recently? (That's a hint.)

 

[Slimsta]

The graph you show is f(x) = xsinx. The function you're investigating is $$g(x)~=~\int_0^x t sin(t)dt$$

How would you ordinarily go about find the local max or min of a function?

Have you learned about the Fundamental Theorem of Calculus recently? (That's a hint.)

$$g(x)~=~\int_0^{pi/4} x sin(x)dx$$

i would look at the graph and see which point looks like local min/max then plug it into the antiderivative of the integral. (which i don't really know how to get because its xsinx...)
so whatever i get for G(x) i will plug that number i got for the local min/max and that will be the value for local min/max.. am i making any sense? lol

and yes i have learned about the Fundamental Theorem of Calculus but how's that helping me?

 

[Char. Limit]

Well, one of the most common applications of the first derivative is in finding the minimum or maximum of a function...

Think about the first derivative as a slope. If $$g(x)$$ is at a min or max, what is the slope?

 

[Mark44]

This integral doesn't have anything to do with your problem. This is not a function of x - it's a constant.

$$g(x)~=~\int_0^{pi/4} x sin(x)dx$$

This is the integral you're interested in
$$g(x)~=~\int_0^x t sin(t)dt$$

What I've been getting at and what Char.Limit made more explicit is for you to look at the derivative of this function. And no, you don't have to evaluate the integral directly. Use the FTC to find g'(x).

i would look at the graph and see which point looks like local min/max then plug it into the antiderivative of the integral. (which i don't really know how to get because its xsinx...)
so whatever i get for G(x) i will plug that number i got for the local min/max and that will be the value for local min/max.. am i making any sense? lol

and yes i have learned about the Fundamental Theorem of Calculus but how's that helping me?

 

[Char. Limit]

Sorry, Mark, but it didn't seem to me as if he fully caught what you were saying...

 

[Mark44]

Sorry, Mark, but it didn't seem to me as if he fully caught what you were saying...

If you're apologizing to me for jumping in, I don't mind. The more the merrier.

 

[Slimsta]

Char. Limit-
"If g(x) is at a min or max, what is the slope? "
its 0.

Mark44-
the FTC just tells me that g'(x)=f(x) (for my case)
which means that g'(x)=xsinx
now g(x) = antiderivative of g'(x) which is <i don't know how to get it, tried everything already>
but how does this help me with any of the question a,b,c or d?

 

[Char. Limit]

Ok... Now what does the first derivative tell you about the min/max points, if you know that the slope of those points must be zero?

 

[Slimsta]

im not sure... i think that it tells me that that min/max point will be positive or negative for g(x)'s graph..
i really have no idea. I am not really good with calc and i feel dumb right now :(

 

[Mark44]

Char. Limit-
"If g(x) is at a min or max, what is the slope? "
its 0.

Mark44-
the FTC just tells me that g'(x)=f(x) (for my case)
which means that g'(x)=xsinx
now g(x) = antiderivative of g'(x) which is <i don't know how to get it, tried everything already>
but how does this help me with any of the question a,b,c or d?

What I've been trying to steer you to is that you don't need to evaluate g(x) directly; all you need is g'(x), which you have already said is equal to x*sinx. If you want to find the max and min values of a function, say g, look at where its derivative g' is zero.

g'(x) = ?
g'(x) = 0 for what x?

 

[Slimsta]

What I've been trying to steer you to is that you don't need to evaluate g(x) directly; all you need is g'(x), which you have already said is equal to x*sinx. If you want to find the max and min values of a function, say g, look at where its derivative g' is zero.

g'(x) = ?
g'(x) = 0 for what x?

g'(x) = xsinx
g'(x) = 0 for x=0,pi, 2pi, 3pi, 4pi

 

[Char. Limit]

So now you know where the min and max are, now you need to figure out which ones are which.

See a way to do that?

 

[Slimsta]

i would know if i had the graph of g(x)..
but i kinda remember from high school that from g'(x) graph, if it goes from + to - then its a local max, and if from - to + its a local min.. but when is it global max/min?