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What is the equation of the normal line of #f(x)=-4x-10 # at #x=-2 #?

Answer 1

#y+2=1/4(x+2)#
or
#y=x/4-3/2#

The normal line at #x=-2# is the line perpendicular to the tangent line at this point. The slope of the tangent line is simply the derivative evaluated at #x=-2#.

#f^'(-2)=-4#

The slope of the line normal to the tangent line is the negative reciprocal of this i.e. #m=1/4#. Now we have a slope, but we still need a point to write the line. So, evaluate the function at #x=-2#.

#f(-2)=-4(-2)-10=-2#

We now have the slope and a point, so use point slope form to acquire the equation of the normal line.

#y+2=1/4(x+2)# or #y=x/4-3/2#

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Answer 2

Elijah Abram

The equation of the normal line of f(x)=-4x-10 at x=-2 is y = 1/4x - 1.

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Answer from HIX Tutor

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.