Math 1271, Summer 2010, Worksheet 19.11. Find the critical points of the function f(x) = 10 + 60x + 9x2− 2x3. Classify them aseither points where the function has a local maximum value or where it has a local minimumvalue using the second derivative test.2. Consider the function f (x) = x8/3− 16x5/3. Same instructions as problem 1.3. The function f (x) is continuous and has the following properties:(a) f0(−4) = 0, f0(2) = 0, f0(8) = 0, f00(1) = 0, and f00(5) = 0.(b) f00(x) > 0 if x < −1, or x > 5. Also f00(x) < 0 if −1 < x < 5.Find the critical points. Use the second derivative test to determine for which values ofx the function f(x) has a local maximum value and for which values of x the function f(x)has a local minimum value.1Math 1271, Summer 2010, Worksheet 19.21. The function f (x) is continuous and has the following properties:(a) f0(−2) = 0, f0(3) = 0, f0(5) = 0, f00(0) = 0, f00(4) = 0 and f00(5) = 0.(b) f0(x) > 0 if −2 < x < 3. Also f0(x) < 0 if x < −2, 3 < x < 5, or x > 5.Find the critical points. Use the first derivative test to determine for which values of xthe function f (x) has a local maximum value and for which values of x the function f (x)has a local minimum value.2. Sketch the graph of a function f(x) which is continuous and has all the properties listed.(a) f0(x) > 0 if x < −3 or x > 5. Also, f0(x) < 0 if −3 < x < 5(b) f00(x) > 0 if x < −8 or 1 < x < 10. Also f00(x) < 0 if −8 < x < 1, or x >
View Full Document
Unlocking...