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NEED SOME CALCULUS HELP!?
Thank you for help and explanations as well. I really want to understand derivatives and how they look graphed.
Question 1:
The figure below shows the graph of four functions. One is the position function of a car, one is the velocity of the car, one is its acceleration, and one is its jerk (derivative of acceleration).
Identify each curve and explain your choices.
(Image attached!)
Question 2:
A supermarket finds that its average daily volume of business V (in thousands of dollars) and the number of hours t the store is open for business each day are approximately related by the formula
V (t) = 20 (1 −(100/100 + t^2)) , 0 ≤ t ≤ 24 .
At what (instantaneous) rate is the daily volume changing when t = 10 hrs?
3 Answers
- ?Lv 73 years agoFavorite Answer
1) A function will have a peak (maximum or minimum) where its derivative has a zero. "a" is the derivative of "b", and "b" is the derivative of "c". The derivative is the slope, so is positive where slope is positive, and negative where slope is negative. "c" is positive everywhere, but its slope is not. "d" has positive slope everywhere, so "c" is probably its derivative. Matching derivatives to definitions, you get
.. (a, b, c, d) = (jerk, acceleration, velocity, displacement)
2) v'(10) = 1
$1000 per hour
_____
v'(t) = 4000t*(100 +t^2)^-2
v'(10) = 4000*10*(100 +10^2)^-2 = 40,000/200^2 = 1
Source(s): https://www.desmos.com/calculator/g6zrn9sz52 - PopeLv 73 years ago
You get one question per ticket. I like question 1.
Velocity is the derivative of displacement, acceleration is the derivative of velocity, and jerk (as you have defined it) is the derivative of acceleration.
Moving from left to right, if a function graph crosses the t-axis, going from positive to negative, then it is the derivative of some other function that is peaking out and beginning to decline. Using that, it appears that function a may be the derivative of b, and b may be the derivative of c.
Notice now that the graph of function d is non-negative throughout. That means it cannot be the derivative of any of the other three, since they all have intervals of decline. Notice also that d is increasing throughout, so only c can be its derivative, because c is positive for any positive t.
c(t) = d'(t)
b(t) = c'(t)
a(t) = b'(t)
d: displacement
c: velocity
b: acceleration
a: jerk
