Find the stationary points of the graph x^3 + y^3 = 3xy +35
Differentiate wrt x to get 3x2 + 3y2dy/dx = 3y + 3x dy/dx Rearrange to get dy/dx = (3x2 - 3y)/(3x-3y2). Set dy/dx =0 and infer y=x2. Substitute in for y into original equation and rearrange to get x6 -2x3 -35 =0. Let p= x3 . Equation in terms of p becomes p2 -2p -35 =0. p=7 or -5. Therefore stationary points are (7(1/3), 7(2/3)) and (-5(1/3), -5(2/3)).
JB
Related Maths A Level answers
All answers ▸A is a function of P . It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P . When P = 24 , A = 36 and when P = 18 , A = 9. Express A in terms of P .
Find the values of the constants a and b for which ax + b is a particular integral of the differential equation 2y' + 5y = 10x. Hence find the general solution of 2y' + 5y = 10x .
When do I use the product rule as opposed to the chain rule?
Solve the following equations. Leave answers in simplest terms a)e^(3x-9)=8. b) ln(2y+5)=2+ln(4-y)