Applications Of Differential Calculus — Quiz 5

Questions in this quiz (10)

1. $$f'(x)=x\cos x+\sin x$$, $$0$$ < $$x$$ < $$4$$$$f$$ has a local maximum when $$x$$ is approximately:

   • $$0.785$$
   • $$1.571$$
   • $$2.331$$
   • $$3.665$$

2. $$f'(x)=x\cos x+\sin x$$, for $$0$$ < $$x$$ < $$4$$.The graph of $$f$$ has a point of inflection when $$x$$ is approximately:

   • $$0.785$$
   • $$1.571$$
   • $$2.331$$
   • $$3.665$$

3. The motion of a particle in a plane is given by the pair of equations$$x=3t$$, $$y=5t-t^2$$The particle moves along:

   • an ellipse
   • a hyperbola
   • a line
   • a parabola

4. The motion of a particle in a plane is given by the pair of equations$$x=3t$$ $$y=5t-t^2$$The speed of the particle at any time $$t$$ is:

   • $$\sqrt{9+(5-2t)^2}$$
   • $$\sqrt{9+(5-t)^2}$$
   • $$3|5-2t|$$
   • $$\sqrt{(3t)^2+(5-2t)^2}$$

5. The motion of a particle in a plane is given by the pair of equations$$x=3t$$ $$y=5t-t^2$$The minimum speed of the particle is:

   • $$2$$
   • $$3$$
   • $$4$$
   • $$5$$

6. The motion of a particle in a plane is given by the pair of equations$$x=3t$$ $$y=5t-t^2$$The acceleration of the particle:

   • depends on $$t$$
   • is always directed downward
   • is constant both in magnitude and direction
   • is always perpendicular to the velocity

7. A particle is moving on the curve $$y=3x-\ln x$$ so that $$\frac{dx}{dt}=-3$$ at all times $$t$$. At the point $$(1,3)$$, $$\frac{dy}{dt}$$ is:

   • $$-9$$
   • $$-6$$
   • $$-3$$
   • $$3$$

8. From the graph of $$g'$$, shown above, $$g'$$:

   • is not continuous at $$x=m$$
   • is continuous but not differentiable at $$x=m$$
   • has a relative maximum at $$x=m$$
   • graph has a point of inflection at $$x=m$$

9. A vertical circular cylinder has radius $$r$$ ft and height $$h$$ ft. If the radius increases at the constant rate of $$3$$ ft/sec and the height increases at the constant rate of $$1$$ ft/sec, then the rate, in square feet per second, at which the lateral surface area increases is:

   • $$2\pi(h+3r)$$
   • $$2\pi(3h+3r)$$
   • $$2\pi(3h+r)$$
   • $$6\pi(r+h)$$

10. Two cars are traveling along perpendicular roads. Car $$A$$ travels at $$30$$ mph and car $$B$$ travels at $$50$$ mph. At noon, when car $$A$$ reaches the intersection, car $$B$$ is $$80$$ miles away and moving toward the intersection. At $$1$$ P.M., the rate, in miles per hour, at which the distance between the cars is changing is:

    • $$-58$$
    • $$-10\sqrt{2}$$
    • $$10$$
    • $$58\sqrt{2}$$