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# C3 Iteration question from a Solomon paper watch

1. I am stuck in the parts B D and E question is from a solomon.

Thanks and Regards
2. for b) plug x=0.5 and x=1 into the equation. If there's a change of sign, then there is a root and hence 0.5<a<1

d) If for example youre value for x4 = 1.234, then you'd plug in 0.5 above and 0.5 below you're answer (into the ORIGINAL equation), e.g. f(1.2335) and f(1.2345). If there's a change of sign then you're value of x is correct to 3dp.

e) ...i'm thinking
3. for D: say your x4 value was 1.351 , you'd do the following: let f(x)=y
then f(1.3505) and f(1.3515), change of sign and curve continuous, therefore root.

for E: you go on till whenever the numbers seem to be drastically changing i.e. from 1.3564 to 5.54 and say that it is divergent.
4. for b)

all you have to do is differentiate y to find dy/dx and because it says stationary point, you know you have to make dy/dx=0 and you just have to rearrange to get the equation x= 1/4(1+ln(8root x)

Step 1 : dy/dx= ½ x^ (- ½) - 4e^ (1-4x)
Step 2: ½ x^ (- ½) - 4e^ (1-4x)=0
Step 3 : rearrange :

½ x^ (- ½) = 4e^ (1-4x)
Simplify the left hand side: 1/(2√x)=4e^ (1-4x)

Take the 2√x to the other side to multiply: 2√x *4e^ (1-4x)
So: 1=8√xe^ (1-4x)

Take the e^ (1-4x) to the left to divide and simplify it :
e^-(1-4x)=8√x

e both sides:

-(1-4x)=ln(8√x)
Then just make the x on the left the subject
5. Hey guyz thanks for the replies

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