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Let f(x) be the function whose graph is shown below. Determine f\'(a) for a = 1,

ID: 2856029 • Letter: L

Question

Let f(x) be the function whose graph is shown below. Determine f'(a) for a = 1, 2, 4, 7. A laboratory study investigating the relationship between diet and weight in adult humans found that the weight of a subject, W, in pounds, was a function, W = f(c), of the average number of Calories per day, c, consumed by the subject. In the statement f(1600) = 160 what are the units of 1600? What are the units of 160? (Think about what this statement means in terms of the weight of the subject and the number of calories that the subject consumes.) In the statement f'(2000) = 0. What are the units of 2000? What are the units of 0? In the statement f^-1 (169) = 2500, what are the unit of 169? What are the units of 2500? What are the units of f'(c) = dW/dc?

Explanation / Answer

1) from graph

f '(1)=0 because graph is horizontal at x=1

f '(2)=0 because graph is horizontal at x=2

graph passdes through (3,3),(5,5)

slope of straight line is (5-5)/(3-3)=1

slope of straight line is constant

so f '(4)=1

f '(7)=0 because tangent is horizontal to parabola at (x,y)=(7,0), infact it is the vertex of parabola.

2)units of 1600 are calories per day

units of 160 are pounds

units of 2000 are calories perday

units of 169 are pounds

units of 2500 are calories per day

units of f '(c) are poundsper (calories per day)