MATH 205 Midterm: MATH 205 KSU Test 3s14 sol

• School: Kansas State University
• Department: Mathematics
• Course: MATH 205
• Professor: All

Document Summary

You can use a note card with formulas prepared in advance. For full credit, show your work in detail. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 total. 100: find the exact global minimum of the function f (x) = x3 12x2 on the interval x > 0. We have f (x) = 3x2 24x. To nd critical points we solve the equation 3x2 24x = 0, that is, x2 = 8x. Since we are looking for x > 0 only, we can divide by x, which gives x = 8. So 8 is the only critical point on the interval x > 0. Since f (1) = 21 < 0, we see that f (x) is decreasing from x = 0 to x = 8 . Next, f (10) = 60 > 0, so f (x) is increasing for x > 8.