Find the equation of the tangent line T(x) to the graph of the given function at the indicated point. y = 2x at (-1, 1) x - 1 T(x) = x+ 2y =1 x Use a graphing calculator to graph the function and the tangent line. y y 15| 15 10 10 5- 5 X -15 -10 10 15 -15 -10 -5 10 15 -5 -5 -10 -10 -15 -15| y y 15 15 10 10 5 5 X -15 10 10 15 -15 -10 -5 5 10 15 -5 -5 -10 - 10 -15 - 15||

In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?

If xis large, which function grows faster, f(x)=2x or g(x)=x2?

Find the equation of the tangent line to the graph of the given equation at the indicated point. x2y2 + 4xy = 12, (2, 1) Use a calculator or computer software to graph the function and the tangent line. y 6 4 2 - 10 -8 -6 2 4 10 - 10 -8 -6 4 - 10 -8 -- -4 2. 4 -10|F -10|| - 10|| y 4 - 10 -8 -6 -4 - 10|F|

The pounds of bananas sold each week at all Metro Seattle Albertsons stores as a function of price, p , in dollars/pound(lb.) is given by q(p) = 100e7.5-1.5p1. Express the Revenue function in terms of p and then find both the first and second derivatives of the revenue function. Type each of these in your text box, using appropriate standard mathematical formatting notation (like that shown above) in Excel. 2. Use Excel over an interval of [0, 6] in increments of .25 to create values for all 3 of your functions from part 1. This is hard! You should be getting the beginning values shown on the next page. Keep at it until you do!! You must create these values by typing in and using the correct formulas. 3. Use Excel to determine exactly where there are any Maximum and/or Minimum values for Revenue. In your text box, explain fully and completely how you determine where to look, and how you know from the First Derivative Test that you have a maximum or a minimum value. 4. Write a…

Sketch the given function and find its domain and range 1 x² + y² z =

Find the first derivative ____, where a, b, c, m and n, are constants. A clear step by step solving of this question would be much appreciated. Thank you!

Question 6 Find the derivative d dx -81-2² A-4x-81-2x² B. 4(In8)x-81-2x² (In8)-81-2x² D-4(In8)x-8¹-2x²

solve the following function and give its domain y= 2(x/x+1)-1

The graph below represents which type of power function of the form y = kx"? Direct Variation with an even r-value & a positive k-value Inverse Variation with an even r-value & a positive k-value Direct Variation with an odd r-value & a positive k-value Inverse Variation with an odd r-value & a negative k-value