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 ?	Choose the most appropriate option:	A) -119	B) -159	C) -110	D) -180	E) -105
Explanation :   Let, the quadratic equation be ax2 + bx + c. So, f(x) = ax2 + bx + c   At x = 0, the value of function is 1.   x = 0, f(x) = 1   ax2 + 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 (ax2 + bx + c) = 2ax + b   At x = 1, 2ax + b = 0.   2a + b = 0.   b = -2a.   Substituting we have a + b = 2, or a + -2a = 2. a = -2. So, b = 4.   So the equation is -2x2 + 4x + 1.   At x = 10, the value is -2 * 100 + 4 * 10 + 1 i.e -159.   Answer : -159
<result>B</result>
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 ?