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How do you find the slope of a tangent line to the graph of the function#F(x)=x^2 - 3# at (-4,13)?

Answer 1

Emily Ammerman

Take the derivative of the function #F(x)#

#F'(x) = 2x#

Plug in your #x# value: #-4#

#F'(-4) = 2(-4) = -8#

This is your slope of the tangent line at point #(-4, 13)#

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Answer 2

Emily Ammerman

To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. The derivative of the function F(x) = x^2 - 3 is given by F'(x) = 2x.

To find the slope of the tangent line at (-4,13), substitute x = -4 into the derivative equation: F'(-4) = 2(-4) = -8.

Therefore, the slope of the tangent line to the graph of F(x) = x^2 - 3 at (-4,13) is -8.

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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.