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Investigating Stationary Points and Finding the Value of the First Derivative at a Particular Point on the Curve

The mathematical solution initially explains how to use calculus to find the stationary points of the curve y = x/(16+x2) by rewriting the equation as a product using index form and using the product rule to find the differential. The stationary points are found by equating the differential to zero and solving the resulting quadratic equation. The second part of the explanation shows how to find the value of the differential of y= (1+e3x)5/3 at x = 1/3ln5 using the chain rule.

 

Graphical solution 1 explains how to use the graphic calculator to find the coordinates of the stationary points of the given function by drawing the graph and using the functions on the calculator to find the coordinates of the maximum and minimum values.

 

Graphical solution 2 explains how to use graphic calculator to find the derivative of the given function at the required value of x to verify the mathematical solution.

 

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