Chapter 2, Problem 2.13P

6). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).

A rental car company has a special deal on one of the available rentals. Let C be the cost, in dollars, of the rental car as a function of the distance d, in miles, it is driven in one day. A. What would the value C(75) represent in this context? B. Is function Cincreasing or decreasing? What are the units of the slope in this situation? C. Identify any maximum or minimum values of the function. What do they represent in this situation? State any assumptions that you make. D. Would the graph of C have any intercepts? What would they represent in this situation? E. Write a rule for C(d), and sketch a graph of the function.

Find the inverse of the given function. f(x) = 5x + 4 .... 11 The inverse of the function is f1 (x) = -X. 5 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Find the derivative of f(x)=32x3+14x2+2x+1 where x=2 . Select one: a. 24 b. 21 c. 6 d. 18

what is the mathematical way to solving this, i used the slope formula but i dont know if that is the way to get answer.

The Augsburg math club paid $200 for fancy souvenir water bottles that they are going to sell next year for $6 each at the Taste of Augsburg during Homecoming Weekend. Define two variables that relate quantities in this story. Which one is the input of this function and which one is the output? Write an equation for your function, and briefly explain why your function is valid.

2.1 Write a well-commented function program for the function x²e¬ª*, using entry-wise operations (such as .* and .*). To get e" use exp(x). Plot the function on [-5,5] using enough points to make the graph smooth. Turn in the program and the graph.

DERIVATIVE    In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols.                                                                                                 Y = X3 -2X2 +1 X -.333 0 .333 .667 1 1.333 1.667 Y               dy/dx               d2y/dx2                 A function is given above.  The table gives several pre-selected values of the independent variable (X).  Use all of these to have enough to answer questions for this assignment.  Calculate the Y value corresponding to each X value in the table.  Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate worksheet, show how you calculated its Y value.  Use these X,Y pairs also if you chose to do the bonus option. Find the critical values among the given X values…

5. Suppose a quadratic function is given by y = f(x) = x29x + 8. (a) Does this function represent an upward or downward facing parabola? Explain. Find the x - coordinate of the vertex (or the equation of the vertical line that intersects the parabola at the vertex) of the parabola.(b) Find the roots of the quadratic function. 1 (c) Using information from (a) and (b) draw a well labelled graph of the parabola (in particular, label the vertex and the roots).(d) In the same graph as (c), draw the parabola if it was instead represented by the function f(x) = x2-9x + 21. How many roots does this parabola have?6. Suppose an inverse demand function is given by p =10 - qd and an inverse supply function is given by p = 4+ 2qs. (a) What is the equilibrium price and quantity combination?  (b) What happens when the price is above or below the equilibrium price? 7. How many solutions does a system of two equations have? Explain clearly and succinctly.