Maths 1999 LC Paper 1

ian.f

I'm having a go at some maths past paper questions and I'm having a hard time. Differentiation is usually easy but I'm just not able to work these ones out

Does anyone wanna help with 1999 P1 Q6(c) or Q7(c) (i) and (ii)

alan4cult

Well for 1999 Q6(C) use the product rule to get f'(x)
Then let f'(x) = 0
Then get f''(x) to show that point is a maximum.

So here goes:
f(x) = xe^-ax

Let u = x -> du/dx - 1
Let v = e^-ax -> dv/dx = -a(e^-ax) [p41 - Log Tables]

Then f'(x) = dy/dx = e^-ax(1) - x(-ae^-ax) [Product Rule]
= e^-ax - axe^-ax
= e^-ax(1 - ax)

Now for max/min f'(x) =0
e^-ax(1 - ax) = 0
1-ax = 0 (e^-ax is not equal to 0)
ax = 1
x = 1/a

y = 1/a(e^-a(1/a))
y = 1/ae

Local Max at (1/a , 1/ae)

You must then show this is a max i.e. f''(x) < 0

For last part solve for x f''(x) = 0 and then get a y value.

I got (2/a , 2/ae^2) for this point.

Guy:Incognito

Ah the memories, I did it that year. Pity the memories arnt what they used to be. Cant remember a thing.