Help again please! :)

Let g(x) = integral of 0 to x f(t) dt, where f is the function whose graph is shown. Answer the following questions only on the interval [0,10].

1) At what values of x does g have a local maximum?

2) At what values of x does g have a local minimum?

3) At what value of x does g have an absolute maximum?

Question

Help again please! :)

Let g(x) = integral of 0 to x f(t) dt, where f is the function whose graph is shown. Answer the following questions only on the interval [0,10].

1) At what values of x does g have a local maximum? 

2) At what values of x does g have a local minimum? 

3) At what value of x does g have an absolute maximum?

anonymous · Answer

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anonymous · Answer

And that is the graph of the function

ganeshie8 · Answer

$$g(x) =   \int_0^x f(t) dt $$

$$\implies   g'(x) =  f(x) $$

ganeshie8 · Answer

So basically you have the graph of derivative of $g$, and u need to find max/min of $g$

ganeshie8 · Answer

Look at the graph, at what points the derivative graph is becoming 0 ?

anonymous · Answer

I put in x=1,5, and 9 but it didn't work

anonymous · Answer

the question is on an website of sorts but it won't accept it

anonymous · Answer

i meant x=1,5,9 for maximums

ganeshie8 · Answer

Nope they're not maximums

ganeshie8 · Answer

At local maximums of $g$,
the graph of $f$ needs to be $0$, and decreasing.

ganeshie8 · Answer

So, Local maximums  occur at x = 2, 6, 10

ganeshie8 · Answer

try this and see if it works..

anonymous · Answer

yeah those worked. but i thought those were inflection points, why would they be the maxs and mins?

ganeshie8 · Answer

cuz you're not looking at funciton

ganeshie8 · Answer

you're looking at `derivative of a function`

ganeshie8 · Answer

whenever derivative equals 0, its a possible max/min point right ?

anonymous · Answer

ah right

ganeshie8 · Answer

see if u can figure out `local minimums`

anonymous · Answer

they would be at 0,4, and 8 because they are increasing and the derivative equals 0?

ganeshie8 · Answer

you got it !!

ganeshie8 · Answer

what about global/absolute maximum ?

anonymous · Answer

that would be x=10 since it has the largest peak out of the whole graph?

ganeshie8 · Answer

Excellent !!

ganeshie8 · Answer

just notice that the areas above and below x-axis almost eat eachother out till x = 8

ganeshie8 · Answer

and after that you got a huge peak of area, so x=10 is indeed the absolute maximum

anonymous · Answer

so just to clarify, the equation is g(x) = integral of 0 to x f(t) dt and the derivative of that is g'(x)= f(x), which is what the graph is because the derivative cancels out the antiderivative?