find the points on the curve where the tangent is parallel?

Question

Find the points on the curve y = x/x+1 where the tangent is parallel to x - y = 2

Answer 1

sidharth has solved the problem correctly and given you the two values for x that satisfy the conditions of the problem.

However, he didn't specify the POINTS on the curve.
They are (0,0) and (-2,-2).

Answer 2

permit P(a, b) be the element at which the given curve has a tangent parallel to the line x + 2y = 10. Slope of the line = - a million/2 y = x^2 + 4x + 2 => dy/dx = 2x + 4 Slope at P = 2a + 4 = - a million/2 => a = - 9/4 Plugging a = - 9/4 in the equation of the curve, b = (-9/4)^2 + 4 * (-9/4) + 2 = 80 one/sixteen - 9 + 2 = - 31/sixteen => the mandatory element is (-9/4, -31/sixteen). Edit: I had purely added the link to Wolfram Alpha jointly as modifying and not replaced something in the respond.

Answer 3

we want points on y=x/(x+1)
at which tangents have slope=1
dy/dx(x/x+1)=1
1/((x+1)^2)=1
x+1=+1,-1
x=0,-2