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What is the equation of the normal line of #f(x)= -3x^2 # at #x=0 #?

Answer 1

Emily Ammerman

#x=0#

#y = -3x^2# is a downward opening parabola, with vertex #(0,0)#.

The tangent line at the vertex is the #x#-axis and the normal line is the #y#-axis.

If you need to do this the long way

#f'(x) = -6x#

The slope of the tangent line at #x=0# is #f'(0) = 0#.

So the tangent line is a horizontal line and the normal line is the vertical line through #(0,0)#. The equation of that line is #x=0#.

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Answer 2

Adam Adkins

The equation of the normal line of f(x) = -3x^2 at x=0 is y = 0.

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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.