Applications Of Differential Calculus — Quiz 6

Questions in this quiz (6)

1. A tangent drawn to the parabola $$y=9-x^2$$ at the point $$(2,5)$$ forms a right triangle with the coordinate axes. The area of the triangle is:

   • $$2$$
   • $$\frac{9}{2}$$
   • $$8$$
   • $$\frac{169}{8}$$

2. Two cars are traveling along perpendicular roads. Car $$A$$ travels at $$35$$ mph and car $$B$$ travels at $$55$$ mph. At noon, when car $$A$$ reaches the intersection, car $$B$$ is $$110$$ miles away and moving toward the intersection. If $$t$$ represents the time, in hours, traveled after noon, then the cars are closest together when $$t$$ is:

   • $$1.10$$
   • $$1.30$$
   • $$1.42$$
   • $$1.75$$

3. The graph shows the velocity of an object moving along a straight line during the time interval $$0\le t\le12$$. The object reverses direction at $$t=$$?

   • $$4$$ only
   • $$5$$ only
   • $$8$$ only
   • $$5$$ and $$8$$

4. If $$f(5)=20$$ and $$f'(x)=\frac{x}{x+2}$$, estimate $$f(5.03)$$ using the line tangent to $$f$$ at $$x=5$$.

   • $$20.02$$
   • $$20.05$$
   • $$20.08$$
   • $$20.12$$

5. A local linear approximation for $$f(x)=\sqrt{x^2+9}$$ near $$x=-4$$ is:

   • $$y=5-\frac{4}{5}(x+4)$$
   • $$y=5+\frac{4}{5}(x+4)$$
   • $$y=5-\frac{3}{5}(x+4)$$
   • $$y=4-\frac{4}{5}(x+4)$$

6. At which labeled point is $$\frac{dy}{dx}=0$$ and $$\frac{d^2y}{dx^2}$$ positive?

   • $$A$$
   • $$B$$
   • $$C$$
   • $$D$$