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?
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?
?
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?
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
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.
(edited 6 years ago)
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