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

Answer 1

#y=-63/4(x+4)-33#

Find the derivative of f(x): Using the quotient rule... #f'(x)=((x)(6x^2)-(2x^3-4)(1))/x^2# Simplifying that... #f'(x)=(4x^3+4)/x^2#

Plug #x=-4# into your #f'(x)# equation: #f'(-4)=(4(-4)^3+4)/(-4)^2=-63/4# This is the slope of the tangent line.

Find your #y# coordinate by plugging #x=-4# into your original equation: #f(-4)=(2(-4)^3-4)/(-4)=33#

Using #x=-4#, #y=33#, and #f'(-4)=-63/4#, form your tangent line equation: #y=-63/4(x+4)-33#

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Answer 2

Adam Adkins

The equation of the line tangent to f(x)=(2x^3 - 4) / x at x=-4 is y = -8x - 4.

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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.