Answer:
- the value of the function changes sign in the interval
- the function is monotonic in the interval
Step-by-step explanation:
All polynomial functions are continuous, so we know from the intermediate value theorem that if the expression on the left changes sign in the interval [-2, 1] then there will be a zero in that interval. If the function is monotonic in the interval, there can only be one zero.
a) For f(x) = x^3 +x +3 = (x^2 +1)x +3, the values at the ends of the interval are ...
f(-2) = (4+1)(-2) +3 = -7
f(-1) = (1 +1)(-1) +3 = 1
The function value goes from -7 to +1 in the interval, so there exists at least one root in that interval.
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b) The derivative of the function is ...
f'(x) = 3x^2 +1
This is positive for any x, so is positive in the interval [-2, -1]. That is, the function is continuously increasing in that interval, so cannot have more than one crossing of the x-axis. There is exactly one root in the interval [-2, -1].
Answer:
y= -4x+16, (4,0), (0, 8)
Step-by-step explanation:
Let us rewrite the equation in slope intercept form, y=mx+b, where m is the slope:
2y= -8x+16
y= -4x+16
Therefore, -4 is the slope.
The x intercept can be found if we substitute 0 into the y:
0= -4x+16
4x=16
x=4
(4,0)
The y intercept can be found if we substitute 0 into the x:
2y= -8*0 +16
2y=0+16
2y=16
y=8
(0,8)
<em>I hope this helps! :)</em>
Answer is 291 minutes of an hour
291 of 60 minutes
97/20 of an hour as a fraction
Step by step
11:24 to 12:00 is 36 minutes
12:00 to 4:15 is 255 minutes
Total minutes passed is 291 minutes
291 minutes over 1 hour
291/60 minutes
Simplify to 97/20 as a fraction
4.85 as a fraction
Answer:
Graph of a one-to-one function if f is a one-to-one function then no two points (x1,y1), (x2,y2) have the Same y-value. Therefore horizontal line cuts the graph of the equation y = f (x) more than omce. Horizontal line test: A graph passes the horizontal line test if each horizontal line cuts the graph at almost once.
