OCR C3 questions

5

hey these have been driving me mad cause have no idea where to start :confused:

1. (a) Find the exact value of the x-co ordinate of the stationary point of the curve y=xlnx <<<<------ does this have something to do with 1/x or something?

(b) the eq of the curve is y = 4x+c/4x-c where c is a non zero constant. show by differentiation that this curve has no stationary points <<<---- no idea

Reply 1

Dekota

silly_billy

(b) the eq of the curve is y = 4x+c/4x-c where c is a non zero constant. show by differentiation that this curve has no stationary points

y = 4x+c/4x-c
dy/dx = [(4x-c).d[4x+c]/dx - (4x+c).d[4x-c]/dx] / (4x-c)²
........ = [4(4x-c) - 4(4x+c)] / (4x-c)²
........ = 4[4x-c - 4x-c] / (4x-c)²
........ = -8c / (4x-c)²

sub (dy/dx = 0)...
........ = -8c / (4x-c)² = 0

But in the question, it mentions that c is a non-zero constant, if it is not equal to 0, then this equation has no solutions hence, no stationary points.

Reply 2

Chewwy

17

a) use product rule to find when dy/dx = 0

b) quotient rule...

post if you need more help.

Reply 3

Dekota

silly_billy

1. (a) Find the stationary point of the curve y=xlnx

y = xlnx
dy/dx = x.d[lnx]/dx + d[x]/dx.lnx (*By product rule)
....... = 1 + lnx

sub (dy/dx = 0), to find stationary points...
...... 1 + lnx = 0
...... lnx = -1
...... x = 1/e

Reply 4

silly_billy

OP

5

Thanks again!

Reply 5

reinainoue

15

Original post

by Dekota

y = 4x+c/4x-c
dy/dx = [(4x-c).d[4x+c]/dx - (4x+c).d[4x-c]/dx] / (4x-c)²
........ = [4(4x-c) - 4(4x+c)] / (4x-c)²
........ = 4[4x-c - 4x-c] / (4x-c)²
........ = -8c / (4x-c)²

sub (dy/dx = 0)...
........ = -8c / (4x-c)² = 0

But in the question, it mentions that c is a non-zero constant, if it is not equal to 0, then this equation has no solutions hence, no stationary points.

thanks bro

u solved a question when i was barely even born that became very useful 14 yrs into the future

(edited 5 years ago)

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