MATH 699 Problem Set 2 (CalcI-CalelI Due February 1, 201 Please do (note log ref

Question

MATH 699 Problem Set 2 (CalcI-CalelI Due February 1, 201 Please do (note log refers to "natural log" (base e)). Instructions: On one sheet of paper, prepare your answer key. Then staple your work to it, clearly showing the work for each problem (in order): 1. art) The figuwe above shows the graph of the derivative f"of a function f, where f is contisuous on the inserval a 4) and diforetiable on the interval (a4). Which of the following pives the orrect ondering of te vaues 2. -1 The graph of the dcrixatise & is shown above, whore h is a real-valued function Which of the following open inncervals costains a value e for which the poist (e.b(e)) is an inflection point of h 7

Explanation / Answer

1.

For this part, you are correct. From the given information We cannot exactly say that which one f(0) or f(4) is greater than one another.

Obviously f(2) is the relative maximum here, so f(2) should be greater than f(0) and f(4) but we cannot exactly say that f(0)>f(4) or f(0)<f(4).

So both the options (c) and (d) could be correct here unless some other information is provided.

2.

Point of inflection is the point on f(x) where f''(x)=0 or we can say this as the point where f'(x) changes its sign from either positive to negative or negative to positive.

In other words it is a point on the graph of f'(x) where we can draw a horizontal tangent.

And that point as seen from the graph of h'(x) lies on the interval (-2,-1)

Hence the first option is correct.

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