Test 4 sols

Test 4 sols - TEST 4 SOLUTIONS 1.[15] Find intercepts....

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TEST 4 SOLUTIONS 1.[15] Find intercepts. intervals on which f is increasing, decreasing; open intervals where f is concave up, concave down; and x-coordinates of all inflection points; also state which points [x- coordinates only] are stationary points, PONDS, and classify as relative maximum or minimum points; specify equation of any vertical tangent. DO NOT SKETCH ( 29 4/3 1/3 f x x x = - [SHOW SIGN GRAPHS AS USED IN CLASS FOR BOTH f and f ′′ ] ( 29 ( 29 4/3 1/3 1/3 1 f x x x x x = - = - so the intercepts are (0,0) and (1,0) ( 29 1/3 2/3 1/3 2/3 2/3 4 1 1 1 4 1 4 3 3 3 3 x f x x x x x x - - = - = - = so there is a POND at x = 0 and stationary point at x = ¼ and the the sign graph for f shows f is increasing on x > ¼, decreasing on x < ¼ [the denominator is always > 0] x = 0 has a vertical tangent there [the derivative doesn’t change sign there] so I guess I mislead you about that – sorry. x = ¼ is a minimum. [No vertical ( 29 2/3 5/3 2/3 5/3 5/3 4 2 2 2 1 2 1 9 9 9 9 x f x x x x x x - - + ′′ = + = + = and this changes sign at both x = 0 and x = - ½ So both these points are inflection points [since f is defined at both] A sign graph of f ′′ shows that f is concave down for -1/2 < x < 0 [ f ′′ < 0 there] and concave up for x < - ½ and x > 0 [ f ′′ > 0 for both of these] 2.[10]Find the absolute maximum and minimum values of ( 29 [ ] cos on / 2, f x x x π = + - Since f is continuous everywhere, the Extreme Value Theorem applies and we are guaranteed both an absolute maximum and an absolute minimum on the closed interval. All
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Test 4 sols - TEST 4 SOLUTIONS 1.[15] Find intercepts....

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