Question

Determine the values of x where the tangent line to f(x)=x^2 over x^2+x-2 how should i do it ?

Answer 1

`x=0` or `x=4`

Explanation:

The tangent is horizontal, where derivative `(df)/(dx)=0`

As `f(x)=x^2/(x^2+x-2)` using quotient rule

`(df)/(dx)=(2x(x^2+x-2)-x^2(2x+1))/(x^2+x-2)^2`

= `(x^2-4x)/(x^2+x-2)^2`

=`(x(x-4))/(x^2+x-2)^2`

Hence, `(df)/(dx)=0` when `x=0` or `x=4`

graph{x^2/(x^2+x-2) [-9.5, 10.5, -4.12, 5.88]}