Question

Find dy/dx given that y² =x(3-x)². State the values of x for which dy/dx is: (a) zero (b) infinite.

answer to (a) ± (3/2√x-(3/2)√x)
answer to (b) is 1

HI CAN YOU SHOW ME STEP BY STEP HOW TO GET X=± (3/2√x-(3/2)√x). AS AM GETTING A DIFFERENT ANSWER (x^2=9/12x)

PS
and part b how do i get the 1 thanks

Answer 1

and so on

Answer 2

thanks just one question what i have done is this

Answer 3

(3x^2-12x+9)/2(x(3-x))^1/2

Answer 4

and then we simplify rational functions, am i on the right track?

Answer 5

hold on ! let me see

Answer 6

why are you doing this step?

Answer 7

i have differentiated the function y² =x(3-x)² using implicit differentiation to get

Answer 8

oh~ i see

Answer 9

2ydy/dx=(3x^2-12x+9)

Answer 10

we then equate dy/dx=0 and solve for x

Answer 11

remembering to put the 2 in the denominator

Answer 12

(3x^2-12x+9)/2(x(3-x))^1/2

Answer 13

also remember that y² =x(3-x)² square root to find y

Answer 14

correct me if am wrong thanks

Answer 15

let me think for a while....

Answer 16

i have made a mistake the denominator should be

Answer 17

(3x^2-12x+9)/2(x^1/2(3-x)) the square root of x not (3-x)

Answer 18

implicit way

Answer 19

i think i have got it :-)

Answer 20

I think this question is not good to use implicit way. so ,you can see the file(1).

Answer 21

check if this is correct we will have (-3/2√x)(x-1)

Answer 22

then when you simplify you get the answer

Answer 23

sorry,my file(10.1) is wrong ,but the file(1) is correct.....so,now, i will rewrite implicit way.....

Answer 24

here is the file (10.1)fixed

Answer 25

sorry i don't get how you got the denominator