AP Calculus AB : Implicit differentiation

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

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Example Question #84 : Applications Of Derivatives

Find the normal line of the curve  at the point 

Possible Answers:

Correct answer:

Explanation:

Use implicit differentiation to calculate the slope of the tangent line:

Simplify:

Subtract x from both sides of the equation:

Divide both sides of the equation by 2y:

Plug in the x and y values from the point into the equation, to calculate the slope of the tangent line: 

Take the negative reciprocal of the slope of the tangent line to calculate the slope of the normal line: 

Plug the slope of the normal line into point slope form: 

Add  to both sides to isolate y: 

Simplify the equation: 

Simplify further: 

Solution: 

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