These are just for practice and don't affect your grade. I'm assuming you've read Ch 4 of the E+P text (especially the thms).
True False. If f is decreasing on I, then f ¢ ¢ < 0 there.
True False. 1/x is decreasing on R (the set of real numbers).
True False. If f has only one relative extrema on I, which is a relative minima, then it is also an absolute minima.
True False. If f is continuous on (a,b) and limf = -¥ as x®a+ and as x® b- then f has an absolute max but no absolute min on (a,b).
True False. If f(x) = x4 + ax3 + bx then f has an absolute min on R.
True False. cot(x) has an abs max on [-p/2,p/2].
True False. tan(x) has an abs max on [-p/4,p/4).
True False. If f ' < 0 on I, then f is decreasing on I.
True False. f(x)=3cos(5x)sin(x) has a stationary point on [0,p].
True False. x1/3 has a vertical tangent line at x=0.
File translated from TEX by TTH, version 3.05. On 14 Mar 2002, 21:21. Written by S.Hudson
Back to Exam Menu