How do you find the linearization of #f(x)=4x^3-5x-1# at a=2?

Answer 1

Find the equation of the tangent line at the point #(2,f(2))#

#f(2) = 21#
#f'(x) = 12x^2-5#, so #f'(2) = 43#

The equation of the tangent line (in point-slope form) is

#y-21=43(x-2)#.

The linearization is

#L(x) = 21 + 43(x-2)#.
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Answer 2

To find the linearization of ( f(x) = 4x^3 - 5x - 1 ) at ( a = 2 ), follow these steps:

  1. Find the value of ( f(a) ) at ( a = 2 ) by substituting ( x = 2 ) into the function ( f(x) ).
  2. Find the derivative ( f'(x) ) of the function ( f(x) ).
  3. Evaluate ( f'(a) ) at ( a = 2 ) to find the slope of the tangent line at ( x = 2 ).
  4. Use the point-slope form of a linear equation ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is the point ( (2, f(2)) ) and ( m ) is the slope ( f'(2) ), to write the equation of the tangent line.

By following these steps, you can find the linearization of ( f(x) ) at ( a = 2 ).

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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.

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.

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.

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.

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