Respuesta :
the derivitive is just the slope
minimum happens when the derivitive goes from negative to positive, imagine a slope of the function, the minimum is where the slope goes from neative to positive, and to get there, it has to pass through 0
max happens when the derivitive goes from positive to negative
increaseing is when the derivitive is positive
so, based on what you said, the slope of f(x) is 0 at x=-3, x=1 and x=2 since those are where the derivitive is 0 (derivitive is just the slope)
A and B are wrong because the derivitive isn't 0 at those points
C is correct because increasing means that the derivitive is positive, and so therefo since the only hoirontal place in between 1 and 2 is 1.5, it must remain positive throughout and not dip down, C is right
D is wrong then
answer is C
The only statement that is true as regards the graph of f ′(x) is;
C: f is decreasing on the interval from x = 1 to x = 2
- We are told that the graph of f ′(x) has x-intercepts at x = –3, x = 1 and x = 2.
Now, f'(x) is simply the derivative of f(x) and the derivative of f(x) is defined as the slope.
- Since x-intercepts of the derivative are at x = –3, x = 1 and x = 2. It means that the values of x that will make the slope to be zero are x = –3, x = 1 and x = 2.
- Now, the minimum for the derivative graph usually happens when the the graph goes from negative to positive. This means that the graph is decreasing when the x-intercepts of the slope is positive
In contrast the graph is increasing when the x-intercepts of the slope is negative.
Let us look at the options;
- Option A; This is not correct because the derivative has to be zero at minimum point.
- Option B; This is not also correct because the derivative has to be zero at maximum point.
- Option C; This is correct because slope is positive when the graph is decreasing and from x = 1 to x = 2 is positive interval.
Read more about graph of derivative of a function at; https://brainly.com/question/2284808
