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How do you find the slope of the tangent line to the graph of the given function #y= -x^-3+x^-2#; x=2?

Answer 1

Luke Alvarez

#"slope "=-1/16#

#"the slope of the tangent is the value of "dy/dx" at x = 2"#

#rArrdy/dx=3x^-4-2x^-3=3/x^4-2/x^3#

#x=2rArrdy/dx=3/16-2/8=-1/16#

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Answer 2

Emily Ammerman

To find the slope of the tangent line to the graph of the function y = -x^-3 + x^-2 at x = 2, we can use the derivative of the function. The derivative of y with respect to x is given by dy/dx. By differentiating the function, we can find the derivative. After finding the derivative, we substitute x = 2 into the derivative to obtain the slope of the tangent line at x = 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.