Show that there is just one point P, on the curve y = x / 1+x where the gradient is 7. find the coordinates of P.
I used the product and chain rule to get:
dy/dx = 3x(x-1)^2 +1(x-1)^3
Then I took (x-1)^2 out of both terms and got:
dy/dx = (x-1)^2(4x-1)
Then I put it equal to 7:
7 = (x-1)^2(4x-1)
But I'm having trouble solving. How can I solve this to find one value of x? Is this equation even correct?
Is this true?