Let F(t) = 4t 1+4t² 1-4t² 1+ 4t² j Using Corollary 12.11, show that F(t)*F' (t) = 0 for all t. i+

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Let f (x, y) = Then range of f is: 5+yx2+y2-1 [1/5, +*I None of these O 10,5) O 5) O 15. +*I O 10, 1/5]

Let f(x, y) = = Evaluate f(5,5) 2 175 - 3x² - 4y²

Consider the function f with domain (-o, 00) whose second derivative is given by J 20(1 +3) (12- 1)3 (a) List all of the possible inflection points. b) Fill out a sign chart for f". t eaton ta noteml e lo daee edt doie (O) c) List any intervals on which f is concave up. d (d d) List any intervals on which f is concave down. = ()-- 0(01 e) Does f any inflection points? If so, where do they occur? os of the given function