#calculus #implicit #differentiation

Implicit Differentiation: Using Calculus to Find Turning Points

An exam question example of how you can use implicit differentiation techniques to solve mathematical problems.

Other fantastic resources on this topic include;
Paul's Maths Notes - Inverse Functions: https://tutorial.math.lamar.edu/class...
Paul's Maths Notes - Implicit Differentiation: https://tutorial.math.lamar.edu/class...

This question was taken from WACE 2021 Specialist Mathematics Examination: https://senior-secondary.scsa.wa.edu....

Example of locating the coordinates of the two turning points on a cubic function. Found by setting f'(x)=0 or dy/dx=0

When I find the quadratic function that results from taking the derivative I will then factorize it so I can use the Null Factor Law to find the x-values that make the derivative equal to zero. however, the quadratic formula would be an adequate alternative solution.

Hope it helps :)

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