Math 1271, Summer 2010, Worksheet 18.11. Find the critical points of the following functions. Use the first derivative test to classifythem as either points where the function has a local maximum value or where it has a localminimum value.(a) f (x) =xx2+16(b) f (x) = 3x4/3− 24x1/32. The function f (x) is continuous and has the following properties:(a) f0(−3) = 0, f0(1) = 0, f0(5) = 0(b) f0(x) > 0 if x < −3, 1 < x < 5 or x > 5. Also f0(x) < 0 if −3 < x < 1.Find the critical points. Determine for which values of x the function f(x) has a localmaximum value and for which values of x the function f (x) has a local minimum value.1Math 1271, Summer 2010, Worksheet 18.21. Consider the function f(x) = x3− 4x2+10x. Let T3(x) denote the function whose graphis the tangent line to the graph of y = f (x) at the point x = 3. Show that f (x) > T3(x) forvalues of x near x = 3.2. Show that f (x) =xx2+4is concave down at x = 2.3. For what values of x is the graph of f (x) = 10 + 60x + 9x2− x3concave up and for whatvalues of x is the graph concave
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