Showing Tangency of y=(x2+x-2)3+3 at (1,3)

[hallowon]

Homework Statement

show that the tangent line to y=(x²+x-2)³+3 at (1,3) is also tangent to the curve at another point

Homework Equations

The Attempt at a Solution

dy/dx=3(x²+x-2)²(2x+1)
at 1
dy/dx = 0
y=mx+b
b=3
y=3

 

[rock.freak667]

Homework Statement

show that the tangent line to y=(x²+x-2)³+3 at (1,3) is also tangent to the curve at another point

The Attempt at a Solution

dy/dx=3(x²+x-2)²(2x+1)
at 1
dy/dx = 0
y=mx+b
b=3
y=3

Then solving the equations y=3 and y=y=(x²+x-2)³+3 will give you two solutions, you know (1,3) is a solution, you just need to get the other solution.