I'm going to bed now, it's 1:45 am here. Bye.
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would use the product rule.
f'g+g'f
+ J*(-1/(x+1)^2)
I don't know how to use th math script..
(x^2+2x+2)/(x+1)^2
]]>I'm rusty at calculus, but I want to learn it again years later.
So this is a product, so there is a rule for that.
What is the derivative of this?
dJ
I'll show my teacher your method.
]]>Add 2 to both sides to solve for Yintercept.
Multiply both sides of equation by Xintercept so as to
solve for the area; you can divide by 2, if you want to
be exact.
What I'm most curious is if this congruency is true at all points.
]]>X intercept = 2
Y intercept = 4
y = mx + b
We know this has to pass through the point (x, y) = (1, 2), so lets plug those in:
2 = m + b, or, m = 2 - b
That didn't seem to get us very far, did it? But at least we have a relationship for m and b, this might come in handy later.
So lets go back. What we want is a general equation for the area of the triangle. Well, we know of the formula 1/2 * base * height. So lets try to find those variables.
The height of the triangle is going to be the y-intercept, b. Easy enough.
The base of the triangle is going to be the x intercept. Since y = mx + b, and y must be 0 (definition of the x-intercept) 0 = mx + b. We want to solve this for x, so that would be x = -b / m.
So the area of the triangle is 1/2 * b * -b/m, or -b^2 / 2m. But wait, isn't this going to be negative? Negative area? Nope, remember the line that we are drawing has a negative slope, so m is negative, making -b^2 / m positive.
So we want to find the least area of the function -b^2 / 2m. Huh, two variables, that's going to be pretty tricky without multi variable calculus. But wait, doesn't m = 2 - b? Told you that would come in handy. So -b^2 / 2 * (2 - b) is the area, or -b^2 / (4 - 2b).
Try to find the minimum for that function. This will tell you what b is, then you can find m because m = 2 - b.
Edit:
And for extra credit, what kind of triangle does this make?
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