Let f x be a cubic polynomial with f 1 = - 10 , f - 1 = 6 , and has a local minima at x = 1 , and f ' x has a local minima at x = - 1 . Then f 3 is equal to .

Step-by-step solution

Let, f x = a x 3 + b x 2 + c x + d Diff w. r. t. ' x ' f ' x = 3 a x 2 + 2 b x + c Again diff. w. r. t. ' x ' f " x = 6 a x + 2 b f " - 1 = 0 - 6 a + 2 b = 0 b = 3 a f ' 1 = 0 3 a + 6 a + c = 0 c = - 9 a f 1 = - 10 - 5 a + d = - 10             … i f ( - 1 ) = 6 11 a + d = 6               … ii From equations i - ii We get a = 1 ,   d = - 5 ,   b = 3 ,   c = - 9 Then, f x = x 3 + 3 x 2 - 9 x - 5 Hen