Question

If `f(x) = 3x^2 -5x`, how do you find and use it to find an equation of the tangent line at the point (2, 2)? I have no idea how to approach this.?

Answer 1

What is it you are asked to find and use?

Answer 2

(I'm assuming the "and use it to find" was redundant)

If `f(x) = 3x^2-5x`

Then the derivative (which gives the slope of the tangent) is
`f'(x) =6x-5`

(using `y` in place of `f(x)` for simplicity)

The slope of the tangent at `(x_1,y_1) = (2,2)`
is
`m=6(2)-5 = 7` (substituting `2` for `x` in the expression for `f'(x)`

The slope-point form of an equation for the line is
`(y-y_1) = m(x-x_1)`

or, in this case
`(y-2) = 7(x-2)`
which simplifies as
`y = 7x -12`