Which of the following is the solution to the inequality below? 9-3x>2(x-3)
1 answer:
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Answer:
See Below.
Step-by-step explanation:
We are given the graph of <em>y</em> = f'(x) and we want to determine the characteristics of f(x).
Part A)
<em>f</em> is increasing whenever <em>f'</em> is positive and decreasing whenever <em>f'</em> is negative.
Hence, <em>f</em> is increasing for the interval:
And <em>f</em> is decreasing for the interval:
Part B)
<em>f</em> has a relative maximum at <em>x</em> = <em>c</em> if <em>f'</em> turns from positive to negative at <em>c</em> and a relative minimum if <em>f'</em> turns from negative to positive to negative at <em>c</em>.
<em>f'</em> turns from positive to negative at <em>x</em> = -2 and <em>x</em> = 1.
And <em>f'</em> turns from negative to positive at <em>x</em> = -1 and <em>x</em> = 3.
Hence, <em>f</em> has relative maximums at <em>x</em> = -2 and <em>x</em> = 1, and relative minimums at <em>x</em> = -1 and <em>x</em> = 3.
Part C)
<em>f</em> is concave up whenever <em>f''</em> is positive and concave down whenever <em>f''</em> is negative.
In other words, <em>f</em> is concave up whenever <em>f'</em> is increasing and concave down whenever <em>f'</em> is decreasing.
Hence, <em>f</em> is concave up for the interval (rounded to the nearest tenths):
And concave down for the interval:
Part D)
Points of inflections are where the concavity changes: that is, <em>f''</em> changes from either positive to negative or negative to positive.
In other words, <em>f </em>has an inflection point wherever <em>f'</em> has an extremum point.
<em>f'</em> has extrema at (approximately) <em>x</em> = -1.5, 0, and 2.2.
Hence, <em>f</em> has inflection points at <em>x</em> = -1.5, 0, and 2.2.
Answer:
Step-by-step explanation:
Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to and
(doesn't matter which you assign) and use the slope formula:
Let:
The slope is equal to:
Therefore, the slope of this line is -1. In slope-intercept form ,
represents slope, so one of the lines must have a term with
in it, which eliminates answer choices A and D.
For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:
Using the slope formula:
Thus, the slope of the line is 1/3 and the other line must have a term with in it, eliminating answer choice C and leaving the answer
*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into