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  • A differentiable function f has one critical number at x = 5. Identify the type of relative extrema of f at the critical number if f ' (4) = -2.5 and f ' (6) = 3. (HINT: First Derivative Test)

  • Let S represent weekly sales of a product. Determine the sign (+ or -) of S' and S'' for each of the following statements:
    a. The rate of change of sales is constant.
    b. Sales are increasing, but at a slower rate.
    c. Sales are declining, but at a slower rate.

Find each derivative. For part b, it is implied that y is a function of x.

a. d/dx (x^3)

b.  d/dx(y^3)


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