Exam 4: Applications of Differentiation

A container holds 6 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of an 0.88 % brine solution to the container and then draining x liters of the well-mixed solution is given as . Find . Round your answer to two decimal places. ​

Find the length and width of a rectangle that has perimeter meters and a maximum area. ​

The graph of f is shown below. For which values of x is zero? ​

Find the open interval(s) on which the function is decreasing in the interval . Round numerical values in your answer to three decimal places. ​

Find the cubic function of the form where and the coefficients are real numbers, which satisfies the conditions given below. ​ Relative maximum: Relative minimum: Inflection point: ​

Determine the open intervals on which the graph of is concave downward or concave upward. ​

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes. ​

Find all points of inflection, if any exist, of the graph of the function . Round your answers to two decimal places. ​

Determine the open intervals on which the graph of is concave downward or concave upward. ​

Analyze the graph of the function . Determine any intercepts, relative extrema, points of inflection and asymptotes. Also determine where the graph is increasing or decreasing and concave up or concave down. Then identify the graph from the choices below. ​

Determine the open intervals on which the graph of the function is concave upward or concave downward. ​

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process. The flow rate R (in liters per hour) at time t (in hours) is given by the linear model . Write the linear model in exponential form. ​

The graph of a function f is shown below. Sketch the graph of the derivative . ​ ​

Identify the open intervals on which the function is increasing or decreasing. ​

Match the function with one of the following graphs. ​

Analyze and sketch a graph of the function . ​

Find the limit. ​ ​

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that . ​

Find the value of the derivative (if it exists) of the function at the extremum point . ​ ​

The measurement of the side of a square floor tile is 14 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the square. ​