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How do you find the slope of the tangent line to the graph of the function #f(x)=x^2-4# at (1,-3)?

Answer 1

Isabella Ackerman

See explanation.

The slope of a tangent line at #(x_0,f(x_0))# is equal to the value of the first derivative at #x_0#: #f^'(x_0)#.

Here we have:

#f(x)=x^2-4#

#f^'(x)=2x#

#f^'(1)=2#

Answer The slope of the tangent line at #x_0=1# is #2#.

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Answer 2

Cameron Alexander

To find the slope of the tangent line at a given point on the graph of a function ( f(x) ), you can use the derivative of the function evaluated at that point.

Find the derivative of the function ( f(x) ) using the power rule: ( f'(x) = 2x ).
Evaluate the derivative at ( x = 1 ) to find the slope of the tangent line at the point (1, -3): ( f'(1) = 2(1) = 2 ).

Therefore, the slope of the tangent line to the graph of ( f(x) = x^2 - 4 ) at the point (1, -3) is 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.