76. If f'(x) = 0 for all x in the domain of f, then ƒ is a constant function. %3D

Suppose that f(x) and g(x) are each one-to-one functions. Suppose also that f(2) = 5, f(5) = 6, g(6) = 5, g(5)= 3.5, and that g(2) = 6. Compute 1. f-¹ (g(6)) 2. f(g-¹ (6)) 3. g=¹(f(2)) = | 4. g(f ¹(5)) = =

Let f(x) be a function with domain (-00, 00). Use the graph of f"(x) below to determine the intervals where f(x) is concave up. y S"(x) I -6 5-4-3-2-1 0 2 3 4 5 6 A. (-5,-1) and (-1,-00) only B. (2,00) only C. (-00,-3), (-1, 1) and (3,00) only D. (-00,-5) only E. (3,00) only

Select the statement that is false about the difference quotient.   The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h The difference quotient is a more general form of the average rate of change of a function on an interval h units long. The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant. As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)). As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).