Answer 1-44 with steps and explanations.

(a) At what value of z will the curve be at its highes (b) Graph this function with a graphing utility to Find the derivatives of the functions in Problems 1-34. 3ã f(x) = ex-x" 5. gx) 500(1-01x) point verify your answer. given by 6. h(x) - 750e04 38. (a) Find the mode of the normal distribution 10, y=1-2e 12, y=e 14, y=e, + elnx 16, y = 2 18, y= 2x + 2 20, p=4qe 22, y = 4(ex)3-4 24, y = ln (c" + 1) 26, y-er' In (4 ) 28. y =- 2x 9, y= 6e 11, y=2e(x1+1), (b) What is the mean of this normal distribution? (c) Use a graphing utility to verify your answer. 15, y=e-1/x 17, y = e-1/x' + e-r 19, s = 12e, 21, y=er_ (ex)' 23. y In (e + 2) 25, y= e-kin (2x) In Problems 39-42, find any relative maxima and minima. Use a graphing utility to check your results. 40, y =- 41 y = x-ex APPLICATIONS 43. Future value If SP is invested fornyearsat 10% 42, y=ex 1 + e ix 29, y = (r" + 4)10 30, y = 32.y-3 34, y = 52-1 compounded continuously, the future value that after n years is given by the function 33, y=4" 35. (a) What is the slope of the line tangent to y xe "at (b) Write the equation of the line tangent to the graph 0.1n S -PeIn (a) At what rate is the future value growing at any ofy = xe-x at x = 1. What is the slope of the line tangent to y = e (1 + e") at x = o? (for any nonnegative n)? (b) At what rate is the future value growing after 36. (a) (e) Is the rate of growth of the future value after (b) Write the equation of the line tangent to the graph greater than 10%? why? is invested at 9%, compounded continuously, is where t is the number of years. of y-r-x/(1 x) at x = 0. 44. Future value The future value that accrues when + e 37. The equation for the standard normal probability dis- tribution is S(t) 700e 09 The mode occurs at the highest point on norm curves and equals thr