`y = 1/(x^2)` Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.

Textbook Question

Chapter 2, 2.2 - Problem 59 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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Rewrite the equation and take the derivative.  Use the power rule.

`y= 1/x^2 = x^(-2)`

`y' = -2x^(-3)`

`y' = -2/x^3`

For horizontal tangent lines, the slope will always equal zero.  Set the derivative function equal to zero.

`0= -2/x^3`

Notice that if we multiplied x-cubed on both sides, we will end up eliminating the x term.  This means that we will not have a solution for x.

Therefore, no horizontal tangent lines exist.

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