Question

Help pleaseeeee

Answer 1

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.

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

Do you need help in this?btw I can't provide help on second part

Answer 3

For a given function f(x) ....
f'(x) gives the slope of f(x) at every point
f''(x) gives the concavity of f(x) at every point

If f''(x) > 0, then f(x) is concave up and the slope is increasing ("U" shape)
If f''(x) < 0, then f(x) is concave down and slope is decreasing (downward facing "U")

Critical points occur at local min/max on f(x)
The slope at these points is zero.
Find concavity of these points by finding if f''(x) is positive or negative, this will tell you whether its a min ("U" shape) or a max( downward facing "U")