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AS Maths Help Differentiation

Help on last question

072C6E77-B59C-4D4E-9048-FE937C311DE3.jpg.jpeg
Original post by officialzak_2001
Help on last question


If f(x)f(x) is increasing then f(x)0f'(x)\geq 0, and it's decreasing then f(x)0f'(x) \leq 0
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RDKGames explained it well. Use that fact to solve the problem.
Original post by officialzak_2001
Help on last question



If f(x)f(x) is increasing then f(x)>0f'(x)>0
Original post by officialzak_2001
Help on last question

072C6E77-B59C-4D4E-9048-FE937C311DE3.jpg.jpeg


If f(x) is increasing over [-1,1] that means for -1<=x<=1 f'(x) >= 0.

So 2x+p >= 0 for those values of x.

Plugging in -1 --> p >= 2.
(edited 6 years ago)
Original post by thekidwhogames
If f(x) is increasing over [-1,1] that means for -1<=x<=1 f(x) >= 0. f'(x) ?

So 2x+p >= 0 for those values of x.

Plugging in -1 --> p >= 2. ?? -1 is not correct

f(x)>0 f'(x) > 0, the inequality is strict.
Original post by BobbJo
f(x)>0 f'(x) > 0, the inequality is strict.


It’s only strict if the function is strictly increasing.

Though at AS level you dont know this difference so OP may as well use the strict version as that’s probably what the question intends
Original post by RDKGames
It’s only strict if the function is strictly increasing.

Though at AS level you dont know this difference so OP may as well use the strict version as that’s probably what the question intends

Oh I see
Original post by thekidwhogames
If f(x) is increasing over [-1,1] that means for -1<=x<=1 f'(x) >= 0.

So 2x p >= 0 for those values of x.

Plugging in -1 --> p >= 2.


Why can’t you sub in 1 instead of -1 and get p is greater or equal to -2
(edited 6 years ago)
Original post by officialzak_2001
Why can’t you sub in 1 instead of -1 and get p is greater or equal to -2


You can, and that gives p2p \geq -2 as you say. But if you consider the fact that at x=1x=-1 we must have 2x+p02x+p \geq 0 as well then we obtain a stricter condition on pp which is p2p \geq 2

Clearly, the range of values which satisfy both inequalities p2p \geq -2 and p2p \geq 2 can be represented by p2p \geq 2

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