Step-by-step explanation:
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Answer:
f(x) > 0 over the interval
Step-by-step explanation:
If f(x) is a continuous function, and that all the critical points of behavior change are described by the given information, then we can say that the function crossed the x axis to reach a minimum value of -12 at the point x=-2.5, then as x increases it ascends to a maximum value of -3 for x = 0 (which is also its y-axis crossing) and therefore probably a local maximum.
Then the function was above the x axis (larger than zero) from , until it crossed the x axis (becoming then negative) at the point x = -4. So the function was positive (larger than zero) in such interval.
There is no such type of unique assertion regarding the positive or negative value of the function when one extends the interval from to -3, since between the values -4 and -3 the function adopts negative values.
Part A: The y-intercept is 5. If you look to the data, when x=0, y=5. This means that the turtle started off 5 miles away from its nest. (at 0 hours, the distance away from his nest was 5 miles)
Part B:Answer=22. Remember, if you take any two distinct points on a line, the slope of the line will be equal to the average rate of change. In short, we're just looking for the slope between the ordered pairs (1,27) and (4,93). The formula for slope is:
The average rate of change between x=1 and x=4 is 22. The average rate of changed describes the rate at which miles is changing with respect the the change in hour.
Part C: Answer=10hours. Since by now we know both the slope and the y-intercept, lets write the equation in slope intercept form and then solve for 225 miles.
y=mx+b
y=22x+5
225=22x+5
subtract 5 from both sides
220=22x
divide both sides by 22
10=x
It would take 10 hours for the turtle to travel 225miles from it's nest.