Exam 4: Applications of the Derivative

Choose the one alternative that best completes the statement or answers the question. -At noon, ship A was 15 nautical miles due north of ship B. Ship A was sailing south at 15 knots (nautical miles per hour; a nautical mile is 2000 yards) and continued to do so all day. Ship B was sailing east at and continued to do so all day. The visibility was 5 nautical miles. Did the ships ever sight each other?

Use l'Hopital's Rule to evaluate the limit. -

Find the extreme values of the function and where they occur. -y =

Find the most general antiderivative. - dx

Use l'Hopital's Rule to evaluate the limit. -

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = - + 1

Find the most general antiderivative. - dx

Find the absolute extreme values of the function on the interval. -f( $\theta$ ) = sin , 0 $\le$ $\theta$ $\le$

Choose the one alternative that best completes the statement or answers the question. -The stiffness of a rectangular beam is proportional to its width times the cube of its depth. Find the dimensions of the stiffest beam than can be cut from a cylindrical log. (Round answers to the nearest tenth.)

Use differentiation to determine whether the integral formula is correct. -

Solve the initial value problem. - = + x, x > 0; y( 1) = 1

Sketch the graph and show all local extrema and inflection points. -y = ln ( 7 - )

Choose the one alternative that best completes the statement or answers the question. -A cylindrical container with a volume of 3? is to be made from two different materials. The material used for the ends costs three times as much as the material for the side. What are the dimensions of the container that minimize the cost of the materials?

Find the absolute extreme values of the function on the interval. -g(x) = 7 - 6 , -2 $\le$ x $\le$ 3

Provide an appropriate response. -Imagine there is a function for which (x) = 0 for all x. Does such a function exist? Is it reasonable to say that all values of x are critical points for such a function? Is it reasonable to say that all values of x are extreme values for such a function. Give reasons for your answer.

Find the most general antiderivative. - dt

Find the extreme values of the function and where they occur. -y =

Express the relationship between a small change in x and the corresponding change in y in the form . -y = sin( 2 )

Determine all critical points for the function. -f(x) = 5 - 3

Find the absolute extreme values of the function on the interval. -f(x) = ln (-x), -6 $\le$ x $\le$ -1