Q1. A curve is such that y =(10
- 3x)(2x + 1)^5. Obtain the coordinates of the stationary
points of the curve and determine their nature.
Is it true that is has only one stationary point? Can anyone
verify it for me? When I checked my answers, there seems to be only
one stationary point...
No, there are two stationary points.
dy/dx would give you
-3(2x+1)^5 + (10-3x)5(2x+1)^4 * 2
= (2x+1)^4 (-6x+3 + 100-30x)
= (2x+1)^4 (-36x+103)
Solving gives you x = -1/2 and 103/36
Q2. Variables N and t are
related by N = ab^t. Linearise the equation in the form Y = mX +
C
I took ln N = ln a + t ln b on everything... will I get the
whole question wrong when I should be taking lg on everything? I
only realised it after the paper 2.
No nothing wrong.
Q3. A curve is such that
(Integral UL 4 LL 0) f(x)dx = 5
Evaluate (Integral UL 4 LL 2)f(x) dx - (Integral UL 0 LL 2)f(x)
dx
UL stands for upper limit and LL stands for lower limit. Will I
get the whole thing wrong if I were to evaluate f(x) which is 5/4
since the question didn't state that f(x) should not be found? AND
the examiner told me that this question has no flaws and there's
something I need to find... so when I evaluate each definite
integral, do I have to take modulus when it is not a 'area under
graph' question? Or is there another trick to this question that I
didn't notice?
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