Applications Of Differential Calculus — Quiz 2

Questions in this quiz (10)

1. The function $$f(x)=x^4-6x^2$$ has:

   • One local minimum and two local maxima
   • One local minimum and no local maximum
   • No local minimum and one local maximum
   • Two local minima and one local maximum

2. The number of inflection points on the graph of $$f(x)=x^4-4x^2$$ is:

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

3. The maximum value of the function$$y=-3\sqrt{5-x}$$ is:

   • $$0$$
   • $$-3$$
   • $$-6$$
   • $$3$$

4. For which curve shown below are both $$f'$$ and $$f''$$ negative?

5. The position of a particle moving along a horizontal line is given by$$s=t^3-3t^2-9t+5$$The object is moving to the right for:

   • $$t$$ < $$-1$$
   • $$-1$$ < $$t$$< $$3$$
   • $$t$$ > $$3$$
   • $$t$$ < $$-1$$ or $$t$$ > $$3$$

6. A particle moves along a horizontal line and its position at time $$t$$ is:$$s=t^4-8t^3+18t^2-2$$The speed of the particle is increasing for:

   • $$0$$ < $$t$$ < $$2$$ or $$t$$ > $$3$$
   • 1 < $$t$$ < 3
   • $$t$$ < 1 or $$t$$ > 3
   • 0< $$t$$ <1 or $$t$$ > 3

7. The displacement from the origin of a particle moving on a line is given by$$s=t^4-6t^3$$The maximum displacement during the time interval $$-1\le t\le5$$ is:

   • $$7$$
   • $$54$$
   • $$125$$
   • $$256$$

8. If a particle moves along a line according to the law$$s=t^5-5t^4$$then the number of times it reverses direction is:

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

9. A spherical balloon is being filled with air at a rate of $$6$$ $$ft^3/min$$. The rate, in square feet per minute, at which the surface area is increasing when the volume is$$\frac{64\pi}{3}$$ $$ft^3$$ is:

   • $$6\pi$$
   • $$3$$
   • $$6$$
   • $$2$$

10. A local minimum value of the function $$y=\frac{e^x}{x^2}$$ is:

    • $$\frac{1}{e^2}$$
    • $$\frac{e}{4}$$
    • $$\frac{e^2}{4}$$
    • $$e^2$$