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

y = - 6x

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.

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

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

and : y - 6 = - 6x - 6 → y = - 6x

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The equation of the line tangent to f(x)=-x^2 -8x - 1 at x=-1 is y = -9x - 10.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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