C1 Maths Help

√3(x −√3) < x +√3

I got x√3 + 3 < x + 3

help Please, Thanks

Try expanding that bracket on the left hand side again and the right hand side should not change!

Then get the x terms on the same side and factorise.

xroot3 - x < 3 + root3

What should I do next ??

Factorise the left hand side.

Then tell me what you have and I will help you finish it.

x(root3 -1 ) < 3 +root 3

Now divide both sides by $\sqrt 3 -1$. This is a positive number so will not affect the direction of the inequality sign. You will need to rationalise the denominator of the right hand side.

Is the answer x<-1


note, say if you were dividing by root3 -10, would you have to swap the sign

First question, no that's really wrong.

$x<\frac{3+\sqrt3}{\sqrt3-1}$

Now rationalise the denominator.

Second question, yes.

is it x < 2root3 +3

Yes.

Is that $y=(x-a)^2$ ?

If so expand the brackets and differentiate.

Compare to the dy/dx you were given.

Yeah
so

(x-a) (x-a)
= x Squared -ax -ax +a squared
= x Squared -2ax + a squared
so dy/dx = 2x -2a + 2a

Ok the last line is wrong. Think about the last term and what you are differentiating with respect to.

Would you differentiate the last term into 0 as it actually a value
so you would then get dy/dx as 2x - 2a

and so -8=-2a
so a =4

Yes.

So how would you draw the graphs ??

Hopefully you know what $y=x^2$ looks like?

$y=(x-4)^2$ is closely connected to it. Think of graph transformations?

I see, i just misread the question. The graph of y=(x-4)squared would move to the left 4 right?

Can you help me to answer this question please

dy/dx= 2x + 1/x2
(a) Use integration to find y in terms of x.

(b) Given that y = 5 when x = 1, find the value of y at x = 1


i can do a, but how do i do b ??
.