For f and g pictured, estimate the following. a . f + g 3 b . f ⋅ g 0 c . g f 3 d . f ∘ g 2 e . The interval s over which f is increasing . f . The interval s over which g is decreasing .
For f and g pictured, estimate the following. a . f + g 3 b . f ⋅ g 0 c . g f 3 d . f ∘ g 2 e . The interval s over which f is increasing . f . The interval s over which g is decreasing .
Solution Summary: The author analyzes the graph of functions f(x)andg
1. Consider the function f(x) whose graph is given below.
Use the graph to determine the following:
2
a) All x for which f'(x) is positive.
b) All x for which f'(x) is negative.
2
-2
c) The x for which f'(x) is zero. (please depict this on the graph)
4. Suppose that the population of a certain collection of rare Brazilian ants is given by
P(t)=(t+100) In(t+2),
Where t represents the time in days. Find and interpret the rates of change of the population on the third day
and on the tenth day.
Find all values of x for f (x)=(x²-4) 4 where the tangent line is horizontal.
5. Find the slope of the tangent line to the graph of f(x)=-√8x+1 at x=1. Write the equation of the tangent
line.
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