Question

Find the equation of the line that is tangent to the graph of f and parallel to the given line? Function Line f(x)=2x^2 4x-y+4=0

Answer 1

The equation is `4x - y - 2=0`

Explanation:

If we convert the equation of the line to slope intercept form, we get:

`4x -y + 4 = 0`
`4x + 4 = y`

Therefore, the slope of this line will be `4`. The slope of the parallel line therefore will be `4`. We will be looking for the value of `x` when the derivative of `f(x)` equals `4`.

`f'(x) = 4x`

Thus

`4 = 4x`

`x= 1`

It follows that `y = 2(1)^2 = 2`

Therefore, the equation of the tangent will be

`y - 2 = 4(x - 1)`

`y = 4x -4 + 2`

`y = 4x - 2`

`0 = 4x - y - 2`

Hopefully this helps!