Please help me with the following questions. Thanks, in advance.

QUESTION 1 A 5-ft-tall person walks toward a wall at a rate of 2 ft/sec. A spotlight is located on the ground 40 ft from the wall. How fast does the height of the person's shadow on the wall change when the person is 10 ft from the wall? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt Ev Ev Av QV ... O WORDS POWERED BY TINY 8 points Save Answer QUESTION 2 Determine all critical points for the function. Use first derivative to find your critical points, as appropriate. (Problems without algebraic/calculus support will not receive credit.) f (x) =20x3-3x5 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt V Ev Av Qv ... Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and SubmitQUESTION 3 Find the absolute extreme values of the function on the given interval. (Problems without algebraic/calculus supprt will not receive credit.) F(x)= = 2 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt Ev Av O WORDS POWERED BY TINY 8 points Save ArewerQUESTION 4 Find the extreme values of the function and where they occur. Use the first derivative tests. Show your work. Use exact answers, not decimal approximations. (Problems without algebraic/calculus support will not receive credit.) Inc For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mack B I Y S Paragraph Arial 10pt O WORDS POWERED BY TINYQUESTION 5 Find the largest open interval where the function is decreasing. Use domain and derivative knowledge. Write answer in proper interval notation (Problems without algebraic/calculus support will not receive credit.) For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I Y S Paragraph Arial 10pt Ev A O WORDS POWERED BY TINYQUESTION 6 For the following function. a. Find the critical points. (Use ordered pairs) b. Find the intervals where the function is increasing or decreasing c. Identify any local minima or local maxima d. Find any inflection points (Use ordered pairs.) e. Find the intervals where the function is concave up or concave down Show all algebraic work - showing first and second derivatives and any equations or inequalities solved in support of your answer. (Hint: For solving rational functions = 0 remember that you only need to set numerator = 0.) x '+2 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I Y S Paragraph Arial 10pt EyQUESTION 7 Use L'Hopital's Rule to evaluate the limit. Be sure to show all work. x2 - 16 lim - 1+4 1-4 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt Ev A O W QUESTION 8 Use L'Hopital's Rule to evaluate the limit. Show work. cos ( 3x) - 1 lim - x 2 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).QUESTION 9 a) State the necessary conditions for the function to satisfy the Mean Value Theorem for the given interval. b) Then determine whether the function meets those conditions. Show your work and clearly state your answer, (Problems without algebraic/calculus support will not receive credit.) R(x) = x /4. [0.4] For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mack B I Y S Paragraph Arial 10pt O WORDS POWERED BY TINY 8 points Save AneverQUESTION 10 Using the following properties of a twice-differentiable function y =/ (x), fill in the last column of the table below (1-6) and then select a possible graph of f (x) . y Derivatives Describe what the derivatives tell you about the shape of the graph over those intervals or about the points. V >0. y >0 4) 2 -22 7' =0, " > 0 5) X32 V >0, y > 0 6) A) B) 16+ 247 C) D)Question Completion Status: *>2 7 > 0, V > 0 6) A) B) 16+ C) D) 24 16 167 -16 24 7QUESTION 11 You are constructing a cardboard box with the dimensions 2 m by 4 m You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions of the box with the largest volume? (Use a decimal approximation for the critical points and your answer. Make sure you use calculus to find your result ) Round to two decimal places. X X X X 2 X X X X 4QUESTION 12 Find the antiderivative of the function. f(x)=e- 12r + cos (x) For the toolbar, press ALT+F10 (PC or ALT+FN+F10 (Mac]. BIVS Paragraph Arial 10pl EVVAY P A WORDS POWERED BY TINY