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Edexcel Maths AS Pure June 2023 Q1(b)

Question 1(b) says to ‘find the range of values of x for which y is decreasing’.

Part 1(a) ask you to find dy/dx which is fine and you end up with 2x^2-7x-4.

I found the roots (x = -1/2 & x = 4) of that equation and then that’s where I got stuck. The markscheme says the answer is -1/2 < x < 4. I can see where it came from but I don’t understand why that is the answer.

Can someone please explain.
(edited 3 months ago)
Reply 1
Original post by wisp.
Question 1(b) says to ‘find the range of values of x for which y is decreasing’.

Part 1(a) ask you to find dy/dx which is fine and you end up with 2x^2-7x-4.

I found the roots (x = -1/2 & x = 4) of that equation and then that’s where I got stuck. The markscheme says the answer is -1/2 < x < 4. I can see where it came from but I don’t understand why that is the answer.

Can someone please explain.

Thats the interval where the gradient is negative (the quadratic is negative) so the function is decreasing.
Reply 2
Original post by mqb2766
Thats the interval where the gradient is negative (the quadratic is negative) so the function is decreasing.

I get that but then isn’t the gradient negative for x < -1/2
Reply 3
Original post by wisp.
I get that but then isn’t the gradient negative for x < -1/2

If you sketched the quadratic ...

You can work out it by considering the sign of each factor (both would be negative in that interval so the product is positive), but a quick sketch is easiest. Note that its a "u" quadratic in this case as a=2>0.

Slighly more generally, the original cubic function must be increasing - decreasing - increasing as x increases (because of the sign of the cubic term and as there are two stationary points).
(edited 3 months ago)

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