Paragraph for Question Nos. 18 to 20 Consider the functions defined implicitly by the equation y3 − 3 y + x = 0 on various intervals in the real line. If x ∈ (− ∞, − 2) ∪ ( 2, ∞ ) , the equation implicitly defines a unique real valued differentiable function y = f ( x ) . If x ∈ (− 2, 2) , the equation implicitly defines a unique real valued differentiable function y = g ( x ) satisfying g (0 ) = 0 . 1. 18. If f (−10√2 ) = 2√2 , then f"( −10√2 ) =   4√2 7332   − 4√2 7332   4√2 733   − 4√2 733   Hint Half-n-half Clue   2. 19. The area of the region bounded by the curve y = f ( x ) , the x-axis, and the lines x = a and x = b , where − ∞ < a < b < − 2, is   b ∫ a x 3 ((f (x))2 − 1 ) dx + b f ( b ) − a f ( a )   b −∫ a x 3 ((f (x))2 − 1 ) dx + b f ( b ) − a f ( a )   b −∫ a x 3 ((f (x))2 − 1 ) dx − b f ( b ) + a f ( a )   b ∫ a x 3 ((f (x))2 − 1 ) dx − b f ( b ) + a f ( a )   Half-n-half Clue   3. 20. 1 ∫ −1 g' ( x ) dx =   2 g (−1)   0   −2 g (1)   2 g (1)   Half-n-half Clue