graphing question help (1 Viewer)

[sssona09]

for the relation x^3 + y^3 =1

a) find the x and y intercepts
do I factorise to (x-1)(x^2 + x +1)
now what?

b) findthe axis of symmetry by exchanging x and y

c) differentiate implicitly and find the stationary and critical point/s

d) discuss the behaviour of the curve as x tends to plus/minus infinity

thank you!!

 

[HeroWise]

for a) it is right you factorise (x-1)(x^2+x+1) and the result would be x = 1
for b) the question literally means swayp x and y values, like
x^3+y^3=1 --> y^3+x^3=1 this proves them to be diagonally symmetrical
for c) its just implicit deifferentiation which results out to be = -x^2/y^2 and simply find the TP and POI
for d) its simple take limits to pos and neg infinity

If you need worked out example, im happiliy willing to do them, just ping me if you dont understand a question specifically

 

[sssona09]

for a) it is right you factorise (x-1)(x^2+x+1) and the result would be x = 1
for b) the question literally means swayp x and y values, like
x^3+y^3=1 --> y^3+x^3=1 this proves them to be diagonally symmetrical
for c) its just implicit deifferentiation which results out to be = -x^2/y^2 and simply find the TP and POI
for d) its simple take limits to pos and neg infinity

If you need worked out example, im happiliy willing to do them, just ping me if you dont understand a question specifically

thank you for the help!!! <3

 

[sssona09]

so do I make dy/dx =0 -----> I found the SP to be (0,1)

do I now find inflection point

edit: solved

 

[HeroWise]

Critical points include Inflexion too ;P
NOTE to OP: ik u solved it but just for people who might find this info useful

 

[InteGrand]

Critical points include Inflexion too ;P
NOTE to OP: ik u solved it but just for people who might find this info useful

Critical points of a differentiable function should just be points where the first derivative is 0. You may want to consult your textbook to see what definition it gives for a critical point.

Wikipedia: https://en.wikipedia.org/wiki/Critical_point_(mathematics)