Question

What is the equation of the line tangent to `f(x)=-x^2 -8x - 1` at `x=-1`?

Answer 1

y = - 6x

Explanation:

To determine the equation of the tangent , y - b = m(x - a ) , require to find m , and (a,b ) a point on the line.

differentiating f(x) and evaluating for x = -1 will give m and evaluating f(-1) will give (a,b)

f'(x) = - 2x -8

hence f'(-1) = - 2(-1) - 8 = - 6 = m of tangent.

now f(-1) =`- (-1)^2 - 8(-1) - 1 = -1 + 8 -1 = 6`

hence ( a , b ) = (-1 , 6 )

equation of tangent : y - 6 = -6(x + 1 )

and : y - 6 = - 6x - 6 → y = - 6x