Question

5. The figure at right is the graph of f ′′ (x), the second derivative of a function f (x). The domain of the function f (x) is all real numbers, and the graph shows
f ′′ (x) for −2.6≤ x ≤3.6.

Answer 1

A. Find all values of x in the interval (−2.6, 3.6) where f ′(x) has a horizontal tangent.
B. Find all values of x in the interval (−2.6, 3.6) where f (x) is concave upwards. Explain your answer
C. Suppose it is known that in the interval (−3.6, 3.6), f (x) has critical points at x =1.37, and x = −0 .97. Classify these points as relative maxima or minima of f (x). Explain your answer.

Answer 2

@AloneS

Answer 3

@nincompoop

Answer 4

@agent0smith Back at it again

Answer 5

@YanaSidlinskiy

Answer 6

A. f"(x) is the slope of the tangent lines for f'(x), so f'(x) has horizontal tangents where f"(x) = 0. Meaning pick out the x-intercepts in the graph

Answer 7

B. f(x) is concave up where f"(x) is positive, so find the intervals where your graph is positive.

Answer 8

C. Use the 2nd derivative test. At a critical point, if f"(x) is positive then the point is a relative minimum, and if f"(x) is negative, the point is a relative maximum.

Answer 9

A. 3,1,-2?

Answer 10

B. 1 and 3?

Answer 11

A is right, but for B you need an interval. Kind of like between what 2 x-values is the graph positive?

Answer 12

between 1 and 3 right?

Answer 13

Between -2 and 1?

Answer 14

yes between -2 and 1, so you'd say (-2, 1)

Answer 15

It's also positive between 3 and 3.6, so (3, 3.6)

Answer 16

jk that doesn't make sense

Answer 17

no, they're asking you whether the points they gave you are max or min.
So look at where x = 1.37. Is the graph positive or negative?

Answer 18

neg

Answer 19

so then it's a max of f(x)

Answer 20

then look at where x = -0.97.
pos or neg?
max or min?

Answer 21

pos, min

Answer 22

Where are you getting these numbers

Answer 23

from your question

Answer 24

part c

Answer 25

Oh right

Answer 26

and yeah it's a minimum

Answer 27

Thank you!