The graph of f ′(x) is continuous and increasing with an x-intercept at x = 5. Which of the following statements must be true?
1 answer:
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Double angle (or half angle, depending how you look at it) identities:
So we have
Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know and
, so it's also the case that
.
Also, the reason we have equality in the last step can be explained like so:
(not unlike the process used to complete the square)
The rate of change, or slope, is the change in y over change in x. To find the slope, pick two points. The slope will be the change in y-coordinates over the change in x-coordinates.
As an equation, this is
To find the slope for function 1, pick any two points (x,y) in the table.
Let's choose (-1, 3) and (-2, 5).
The slope is
.
Let's choose (-1, 0) and (0, 4) for the two points for function 2.
The slope is
.
You want to compare the magnitude (without negatives) of the slope when comparing the greater rate of change/slope. In other words, you take the absolute value of each slope.
The magnitude of function 1's slope is 2.
The magnitude of function 2's slope is 4.
As an equation, this is
To find the slope for function 1, pick any two points (x,y) in the table.
Let's choose (-1, 3) and (-2, 5).
The slope is
Let's choose (-1, 0) and (0, 4) for the two points for function 2.
The slope is
You want to compare the magnitude (without negatives) of the slope when comparing the greater rate of change/slope. In other words, you take the absolute value of each slope.
The magnitude of function 1's slope is 2.
The magnitude of function 2's slope is 4.