# Thread: Max/Mins Without Numerical Values (On Graph)

1. ## Max/Mins Without Numerical Values (On Graph)

These are two different types of max min problems but I understand that they go on a graph instead of being the usual rectangle with a given value question.

2. Originally Posted by SportfreundeKeaneKent
These are two different types of max min problems but I understand that they go on a graph instead of being the usual rectangle with a given value question.

For the first:

two lines are parrallel if they have the same slope. the slope of the line is 9. so we simply want to find the $x$'s that make the tangent lines to the curve have a slope of 9. the derivative gives the formula for the slope of the tangent line.

$y = x^3 - 3x^2$

$\Rightarrow y' = 3x^2 - 6x$

Now we simply solve:

$3x^2 - 6x = 9$

i leave that to you

3. Originally Posted by SportfreundeKeaneKent
These are two different types of max min problems but I understand that they go on a graph instead of being the usual rectangle with a given value question.

see http://www.mathhelpforum.com/math-he...ma-minima.html as a hint for the second

i assume you remember how to maximize a function

4. A question about the one with the tangent. Would you sub x=-1,3 (the two values I obtain after factoring and finding x) into y=x^3-3x^2 or into y=9x+7?

I'm guessing that you'd sub it into y=9x+7 to obtain the two points to be (3,34) and (-1,-2)

5. Originally Posted by SportfreundeKeaneKent
A question about the one with the tangent. Would you sub x=-1,3 (the two values I obtain after factoring and finding x) into y=x^3-3x^2 or into y=9x+7?

I'm guessing that you'd sub it into y=9x+7 to obtain the two points to be (3,34) and (-1,-2)
we want two points ON THE CURVE, therefore you would plug them into the original function to obtain the y-values for the points. we wouldn't sub them into the line, unless we knew that the line intersected with our curve exactly at the points where the slope of the curve is 9. so just plug them into $y = x^3 - 3x^2$

why did you think you would plug it into the line?

6. Oh wait, I wrote it the wrong way around. So the points are just (-1,-4) and (3,0)

7. Originally Posted by SportfreundeKeaneKent
Oh wait, I wrote it the wrong way around. So the points are just (-1,-4) and (3,0)
correct

8. ## tangent lines

tangent lines