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How do you find the linearization at x=2 of #f(x) = 3x - 2/x^2#?

Answer 1

Isabella Ackerman

Taylor: #11/2 + 13/4(x - 2) + O(x-2)^2#

#f'(x) = 3 + 2/x^3 => f'(2) = 3 + 2/8 = 13/4#

#L(x) = 13/4x + b and L(2) = f(2)#

#f(2) = 6 - 2/4 = 11/2#

#13/4 * 2 + b = 11/2 => b = 1#

The tangent line at x = 2 is #L(x) = 13/4 x + 1#

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Answer 2

Samantha Adkison

To find the linearization at ( x = 2 ) of ( f(x) = \frac{3x - 2}{x^2} ), follow these steps:

Find the first derivative of ( f(x) ).
Evaluate the derivative at ( x = 2 ) to find the slope of the tangent line.
Find the value of ( f(x) ) at ( x = 2 ) to find the ( y )-intercept of the tangent line.
Write the equation of the tangent line using the slope and ( y )-intercept found in steps 2 and 3.

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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.