So differentiated instruction is a logical way to achieve the goal of content acquisition. Fermats theorem if f has a local maximum or minimum atc, and if f c exists, then 0f c. Techniques of differentiation classwork taking derivatives is a a process that is vital in calculus. The trick is to differentiate as normal and every time you differentiate a y you tack on a y. A free variable is used to assert that an equation is valid for a range of values. But theres a parallel logic in differentiation that functions at a deeper level. On completion of this tutorial you should be able to do the following. Applications of differentiation 2 the extreme value theorem if f is continuous on a closed intervala,b, then f attains an absolute maximum value f c and an absolute minimum value f d at some numbers c and d in a,b. This is a technique used to calculate the gradient, or slope, of a graph at di. Rememberyyx here, so productsquotients of x and y will use the productquotient rule and derivatives of y will use the chain rule. In order to take derivatives, there are rules that will make the process simpler than having to use the definition of the derivative. Apply newtons rules of differentiation to basic functions. However, if we used a common denominator, it would give the same answer as in solution 1.
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