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1. -RM-
2. (Original post by UCASLord)
Find the range of the below equation, also indicating whether it is a one-to-one function or a one-to-many function.

f(x) = x^2 - 7x + 10, x ∈ R

I differentiated:

dy/dx = x - 7
x = 7
d^2y/dx^2 = 1

So it's a minimum.

But it's not actually a minimum. I noticed that the point where x = 7 is at y = 10, the same if x = 0. Now, if I take the point between these two coordinates, I get 3 1/2, which is the actual location of the minimum.

My question is why doesn't this differentiation give me the minimum point?
?
3. (Original post by UCASLord)
Find the range of the below equation, also indicating whether it is a one-to-one function or a one-to-many function.

f(x) = x^2 - 7x + 10, x ∈ R

I differentiated:

dy/dx = x - 7
x = 7
d^2y/dx^2 = 1

So it's a minimum.

But it's not actually a minimum. I noticed that the point where x = 7 is at y = 10, the same if x = 0. Now, if I take the point between these two coordinates, I get 3 1/2, which is the actual location of the minimum.

My question is why doesn't this differentiation give me the minimum point?
I guess what _gcx is trying to point out is that
4. -RM-
5. -RM-
6. (Original post by UCASLord)
Quick question though: is it a complete coincidence that I got the next point where y = 10, or is there a reason behind it?
Huh? What do you mean?

as other have pointed out. So setting this gives which is where the min point is. You get at the y-intercept, which is nothing to do with it. It's a parabola so every other y coordinate point except the minimum will have two distinct x coordinates to go with it. In this case, x=0 and x=7.

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