Question

How do you find the equation of the line tangent to the graph of `(2x^3 - 1) / (x²)` at the point (1,1)?

Answer 1

`y = 4x-3`

Explanation:

`(2x^3-1)`/`(x^2)`= `2x-1/x^2`
the derivative is slope of the tangent and is `2+2/x^3`
at x=1 the slope is 4
as point is (1,1) and slope is 4
general equation of a line is
`y = mx+c`
given `m=4& (x,y)=(1,1)`
substituting
`1=4+c`
`c=-3`
the equation of tangent is
`y = 4x-3`