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B.2.1b – Graphical Differentiation

B.2.1b – Graphical Differentiation. Calculus - Santowski. Working Backwards – From f’ to f. You will be given a series of graphs which represent the derivative of a function. (a) Using the graph of the derivative, state & justify the: (i) intervals of increase/decrease of f(x)

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B.2.1b – Graphical Differentiation

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  1. B.2.1b – Graphical Differentiation Calculus - Santowski

  2. Working Backwards – From f’ to f • You will be given a series of graphs which represent the derivative of a function. • (a) Using the graph of the derivative, state & justify the: • (i) intervals of increase/decrease of f(x) • (ii) extrema of f(x) • (iii) intervals of concavity of f(x) • (iv) inflection points of f(x) • You must then sketch the original function

  3. Working Backwards – From f’ to f • Graph #1

  4. Working Backwards – From f’ to f • Graph #2

  5. Working Backwards – From f’ to f • Graph #3

  6. Inflection Points and Concavities • Describe the concavity of the following graphs and find the points of inflection (if any). You will first do all the work on the TI-89 and then algebraically develop the solutions.

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