Question: A differentiable function f has one critical number at x = 5. Identify the type of relative extrema of f at the critical number if

  • 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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