Question

Use the Concavity Theorem to determine where the given function is concave up and where it is concave down. Also find all inflection points. 12) g(x) = 2x3 + 2x + 7 A) Concave up for all x no inflection points B) Concave up on (0, concave down on ( 0) infection point (0.7) c) Concave up on ( 0), concave down on (0 ); Inflection point (0,7) D) Concave down for all no inflection points Provide an appropriate response. 13) Find f(x) for f(x) - 54-6x27 A)(x) = 60x2.12% C)(x) = 80x2.12 B) rix) = 20x2.12 D)(x) = 20x2. 12x Find the largest open interval where the function is changing as requested. 14) Increasing 2.1 A) (0 ) B)(- 1) C)(- 0) D) (1.-) Solve the problem. 15) The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately R(x) = 480x -0.02x2 and C(x) = 120x + 100.000, where x denotes the number of clocks made. What is the maximum annual profit? A) $1.620.000 B ) $1.820.000 C) $1.720.000 D) $1.520.000 Find the intervals where the function has the indicated concavity. Give the x coordinates of Inflection points 16) Concave upward A) (0 C) - ): x=0 3) = 0 B) (- 3 X =0 D) (0.); no inflection points Find the absolute maximum and absolute minimum values of the function. If they exist, on the indicated interval 17)f(x)=x2-12x 40: 12. 81 A) Absolute maximum: 4 B) Absolute maximum: 20, absolute minimum: 4 C) Absolute maximum: 8, absolute minimum: 4 D) Absolute maximum: 20, absolute minimum: 8 Provide an appropriate response. 18) A company manufactures and sells x pocket calculators per week. If the weekly cost and equations are given by CIX) - 8,000 + 5x p=14- OSX 25,000 4.000 Find the production level that maximizes profit. A) 14.000 pocket calculators per week B) 2000 pocket calculators per week C) 18,000 pocket calculators per week. D) 8000 pocket calculators per week

Answer 1

912 - 912) = 2x² + 2x + 7 -6 Differentiate wigito Get atson we have. - q' (8) = 672+2 - Again Diffenen Haute writi age of egm2), we here 9 "(x) = 123 - 3) for critical point for alw, 4112020 1221 70 = 250 So Inflection point for g(x) is azo fere ao q"(W) Lo and for xro q"(2) 70 So Curve (x)is concave downward on(-20) __and cwive 2(X) is concave_upward en (0,03 Ley

(3) $100= 5x4 -622+7 +(94) z 2003-123 ? f2) = 60.32-12 fere option.com