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# Why is this a decreasing function?

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1. In this question:
'For what values of x is y = x2 - 2x + 5 a decreasing function?'

i don't understand why the answer is x ≥ 1 (given in the answers)

my method:

dy/dx = 2x - 2

so x = 1 which will make y = 4 and the turning point (1,4)

so if i put in x = 0 (x ≤ 1), y is 5, and the gradient -2
and if i put in x = 2 (x ≥ 1), y = 5 but the gradient is +2

therefore, wouldn't the decreasing function of x be x ≤ 1, because that is when gradient is negative for those values, so the y value is decreasing?

any help would be appreciated
2. (Original post by lily628)
In this question:
'For what values of x is y = x2 - 2x + 5 a decreasing function?'

i don't understand why the answer is x ≥ 1 (given in the answers)

my method:

dy/dx = 2x - 2

so x = 1 which will make y = 4 and the turning point (1,4)

so if i put in x = 0 (x ≤ 1), y is 5, and the gradient -2
and if i put in x = 2 (x ≥ 1), y = 5 but the gradient is +2

therefore, wouldn't the decreasing function of x be x ≤ 1, because that is when gradient is negative for those values, so the y value is decreasing?

any help would be appreciated
Your result of x <= 1 is correct. The answer given in whatever book/resource you got the question from is mistaken.
3. (Original post by lily628)
In this question:
'For what values of x is y = x2 - 2x + 5 a decreasing function?'

i don't understand why the answer is x ≥ 1 (given in the answers)

my method:

dy/dx = 2x - 2

so x = 1 which will make y = 4 and the turning point (1,4)

so if i put in x = 0 (x ≤ 1), y is 5, and the gradient -2
and if i put in x = 2 (x ≥ 1), y = 5 but the gradient is +2

therefore, wouldn't the decreasing function of x be x ≤ 1, because that is when gradient is negative for those values, so the y value is decreasing?

any help would be appreciated
The answers are incorrect, you are correct.
4. (Original post by HapaxOromenon3)
Your result of x <= 1 is correct. The answer given in whatever book/resource you got the question from is mistaken.
(Original post by Zacken)
The answers are incorrect, you are correct.
ohh that's a relief, thank you both!
5. (Original post by lily628)
ohh that's a relief, thank you both!
No worries.

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