Question

3 questions to be checked calculus help @vocaloid

Answer 1

b

Answer 2

a

Answer 3

a

Answer 4

@Vocaloid

Answer 5

@jimthompson5910 sorry to bother but would you mind looking over these? the material isn't very fresh in my mind :(

Answer 6

For problem 1, look at how the red curve's roots correspond to the green curve's local extrema. This shows that the red curve is the derivative graph to the green one

Because the red curve is curve B, and the green is curve C, this suggests C is the derivative of B

Therefore you are correct in saying the answer is choice 2. This is the only answer choice where curve C is followed right after curve B in terms of listing the functions f, f ' and f ''

Answer 7

Problem 2 is also correct when you selected choice A

F ' (2) is some negative number because f(x) is below the x axis
F ' (x) = f(x) by the fundamental theorem of calculus
So statement I is false

F(3) < F(4) is true because F(4) involves all of F(3)'s area plus the portion under the curve from x = 3 to x = 4, so statement II is true

F(1.5) is not a local min, that would be F(3) because the F(x) graph bottoms out after adding the most negative area we can under f(x), so statement III is false

Answer 8

any ideas on the last one? I've never personally done this approximation method so I didn't want to mislead them or something

Answer 9

The idea for problem 3 is to plot all of the points given, then draw trapezoids to get what you see in the attached image. Find the area of each trapezoid and then add up the individual areas. You can also use the formula mentioned here
http://www.mathwords.com/t/trapezoid_rule.htm
to get the same result

You should get 115.5 as the total area. Once you know the total area, you divide that by 13-3 = 10 as this is the horizontal width from x = 3 to x = 13

You should get 11.55 as the result, so choice A is correct for problem 3

Answer 10

The idea I used for problem 3 is
\(\Large \displaystyle M = \frac{1}{b-a}\int_{a}^{b}f(x)dx\)
which computes the average value of f(x) on the interval [a,b]