X X Let f t 2t 14 and consider the two area functions A x f t dt and F x f t dt Complete parts a c 1 dl and Fix S 10 Use

Question

X X Let f t 2t 14 and consider the two area functions A x f t dt and F x f t dt Complete parts a c 1 dl and Fix S 10 Use geometry to find an expression for A x when x 27 x 14x 49 Type an expression using x as the variable b Evaluate F 11 and F 12 Then use geometry to find an expression for F x for all x2 10 The value of F 11 is 7 Simplify your answer The value of F 12 is 16 Simplify your answer Use geometry to find an expression for F x when x 2 10 14x 40 Type an expression using x as the variable c Show that A x F x is a constant and that A x F x f x First prove A x F x is a constant Given A x x 14x 49 and F x x 14x 40 subtract F x from A x The value of A x F x is 9 Simplify your answer Now prove that A x F x f x Given A x and F x take the derivative of A x and F x respectively and compare the results A x x 14x 49 Simplify your answer Do not factor

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