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Calculus 4E-Ch 14&15
Calculus 4E-Ch14:Using the Power Rule & Ch15:Derivatives & the Problem of Change
| Question | Answer |
|---|---|
| The general form of a power function is f(x) = | Kx^n |
| A POLYNOMIAL can only have_________________ integers as exponents, whereas there is NO such restriction on the exponents of power functions. | positive |
| For any power function f(x)=Kx^n, its derivative f'(x)= | nKx^n-1 |
| For y(x)= f(x) + g(x) + u(x) . . . . , the derivative is | y'(x)= f'(x) + g'(x) + u'(x) . . . . |
| Galileo's Law of Free Fall | d(t) = 16t^2 |
| The derivative of Galileo's Law of Free Fall is the formula for __________________________ velocity. | instantaneous |
| The derivative of d(t) = 16t^2 is | d'(t) = 32 t |
| The derivative of the formula for INSTANTANEOUS velocity is the formula for ____________________________. | acceleration |
| The distance function with respect to time tells us how many feet a ________________ object has fallen after ______ seconds. | dropped, t |
| the rate of change of DISTANCE (or location) with respect to TIME | velocity |
| Velocity is measured in _________ per second. | feet |
| Acceleration is the rate of CHANGE of _______________________. | velocity |
| d"(t) = v'(t) = a(t) = | 32 ft/s per second |
| Acceleration is measured in | feet per second per second (or ft/seconds squared). |
| A falling object picks up speed at a rate of 32 ft/second | every second. |
| average acceleration | Δv/Δt |
| A NEGATIVE sign added to Galileo's Law of Free Fall indicates that a dropped object is moving _____________________. | downward |
| The law of fall tells us how far an object has fallen but it can only tell us an object's distance above the ground once we know | WHERE the object was dropped from. |
| For the function h(t) = -16t^2+12, the -16t^2 represents | how FAR the object has fallen. |
| For the function h(t) = -16t^2+12, the +12 represents | the initial HEIGHT the object from which the object was dropped. |
Created by:
MrsHough
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