Question

What is the equation of the line tangent to `f(x)= 3x^2 - 12x-5` at `x=-1`?

Answer 1

`y=-18x-8`

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 line"`

To find a point on the tangent, evaluate f( -1)

`f(-1)=3(-1)^2-12(-1)-5=3+12-5=10`

`rArr(-1,10)" is a point on the tangent line"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)("slope" =m=f'(x))color(white)(2/2)|)))`

`rArrf'(x)=6x-12rArrf'(-1)=-6-12=-18`

`rArry-10=-18(x+1)rArry-10=-18x-18`

`rArry=-18x-8" is the equation of the tangent line"`