a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?
explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b
add(add(multiply(power(10, const_2), negate(subtract(3, 1))), multiply(subtract(subtract(3, 1), negate(subtract(3, 1))), 10)), 1)