# What is the equation of the line normal to # f(x)=-x/(x+4)# at # x=6#?

y = 25 x

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To find the equation of the line normal to f(x)=-x/(x+4) at x=6, we need to determine the slope of the tangent line at x=6 and then find the negative reciprocal of that slope to obtain the slope of the normal line.

To find the slope of the tangent line at x=6, we can take the derivative of f(x) with respect to x and evaluate it at x=6.

The derivative of f(x)=-x/(x+4) is given by f'(x) = (4x+16)/(x+4)^2.

Evaluating f'(x) at x=6, we get f'(6) = (4(6)+16)/(6+4)^2 = 40/100 = 0.4.

The slope of the tangent line at x=6 is 0.4.

To find the slope of the normal line, we take the negative reciprocal of 0.4, which is -2.5.

Now, we have the slope of the normal line, -2.5, and the point of tangency, (6, f(6)).

Using the point-slope form of a line, the equation of the line normal to f(x)=-x/(x+4) at x=6 is y - f(6) = -2.5(x - 6).

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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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