E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
Answer:
0.364
Step-by-step explanation:
3 is in the tenths place
6 is in the hundredths place
4 is in the thousandths place
so it's 0.364 because it goes up to the thousandths place
Answer:
81 Pesos
Step-by-step explanation:
Use a proportion.
$3 is to 2 Pesos as $121.10 is to x Pesos.
3/2 = 121.1/x
3x = 2 * 121.1
3x = 242.20
x = 80.7333...
Answer: 81 Pesos
The answer is C) 3 x 10^4
Answer:
It takes more time on moon for the rock to fall.
Step-by-step explanation:
Given that:
Time it takes for rock to fall d meters on earth = √0.45d
Time it takes for rock to fall d meters on moon = √1.11d
For a rock to fall 50 meters:
On earth :
Time = √0.45*50 = 4.7434164 seconds
On moon :
Time = √1.11*50 = 7.4498322 seconds
Time on moon > Time on earth
Hence, It takes more time on moon for the rock to fall.
