Question

How do you find the slope of a tangent line to the graph of the function `f(x)=2x^2-8x+4` at (5,14)?

Answer 1

`y=12x-46`

Explanation:

The equation of the tangent in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the tangent"`

`color(orange)"Reminder"`

The slope of the tangent is `dy/dx` evaluated at x = 5

`rArrdy/dx=4x-8`

`x=5 : dy/dx=20-8=12=m`

Substitute m = 12 and `(x_1,y_1)=(5,14)" into the equation"`

`y-14=12(x-5)rArry-14=12x-60`

`rArry=12x-46" is the equation of the tangent"`