Math 1271, Summer 2010, Worksheet 11.11. Let f (x) = x3+ g(5x2+ 2). Find f0(2) given that g(2) = 8, g0(2) = −6, g(20) = 11,g0(20) = 4, g(22) = 5, and g0(22) = 9.2. Let f(x) =pg(x2). Find f0(3) given that g(3) = 5, g0(3) = 8, g(6) = 7, g0(6) = −4,g(9) = 16, and g0(9) = 5.3. Let f(x) = x2g(1x). Find f0(2) given that g(−14) = 5, g0(−14) = 9, g(12) = −6, g0(12) = 8,g(2) = 4, and g0(2) = 11.4. Let f(x) =1+tan xx+sin x. Find f0(x) and simplify.1Math 1271, Summer 2010, Worksheet 11.21. Consider the function f (x) defined as follows: Given a value of x, the correspondingvalue of y is the solution of the equation y2− 6y + 4x = 8 such that y ≤ 3. Find f0(4) andf0(−2).2. (a) Consider the function g(x) defined as follows: Given a value of x, the correspondingvalue of y is the solution of the equation x2+ y2+ 4x −10y = 71 such that y ≤ 5. Find g0(4)and g0(−10).(b) The function g(x) can be defined explicitly as g(x) = 5 −√96 − 4x − x2for −12 ≤x ≤ 8. Use this explicit form of g(x) to find g0(x) and g0(−10).3. Suppose y is defined as a function of x implicitly by x3y2= 4x2y + 24. Find theequation(s) of the tangent line(s) at all points on the graph of the equation with x coordinatex =
View Full Document
Unlocking...