1) At 2:00pm a car\'s speedometer reads 50mph, and at 2:10pm it reads 70mph. Use
ID: 2827620 • Letter: 1
Question
1) At 2:00pm a car's speedometer reads 50mph, and at 2:10pm it reads 70mph. Use the Mean Value Theorem to find an acceleration the car must achieve.
Answer(in mi/hr^2) =?????
2) Suppose that f(0) = 2 and f'(x) <= 7 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be.
Answer: f(4) <= ???
3) Suppose f(x) is continuous on [2,8] and -2 <= f'(x) <= 5 for all x in (2,8). Use the Mean Value Theorem to estimate f(8)-f(2).
Answer: ??????? <= f(8)-f(2) <= ?????
Explanation / Answer
1)
You just need to show that there's a point in that interval where the acceleration (slope) is 120 mph... Which you can simply prove by finding the slope in this instance.
Here, you would find the slope as such: (70 - 50) mph/ (10) mins = 20 mph / (1/6) hr = 120 mph...
And by the definition of MVT ... you just showed that there is a point in that interval where the acceleration is 120 mph.
2)
conditions:
i) Point (0, 2) is on the graph of f(x)
ii) The slope of the tangent line f'(x) is never steeper than 7
if f(x) maintained it's maximum slope as x goes from 0 to 4, it would be a straight line of slope 7. since (0, 2) is on the graph, the line would be y = 7x + 2
so the maximum of f(x) when x = 4, would be
y = 7(4) + 2
..= 30
Mean Value Theorem i am thinking of does not have a way of being applied because we are not given any function or conditions for a curve
1/(b - a) [ ?f(x)dx ](b, a)
3)
-24 to 30
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