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What is the equation of the line normal to # f(x)=4x^2-3x # at # x=1#?

Answer 1

#y=-1/5x+6/5#

The derivative is #f'(x)=8x-3# so that #f'(1)=5#. The slope of the normal line is the opposite reciprocal of this, which is #-1/5#.

Since the point #(1,f(1))=(1,1)# is on the line, the equation of the line is #y-1=-1/5(x-1)#, which is equivalent to #y=-1/5(x-1)+1# and #y=-1/5x+6/5#.

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Answer 2

Aurora Alvarado

The equation of the line normal to f(x)=4x^2-3x at x=1 is y = -9x + 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.