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 4 months ago)

Reply 1

mqb2766

21

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

wisp.

OP

1

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

mqb2766

21

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 4 months ago)

Edexcel Maths AS Pure June 2023 Q1(b)

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