Latest CAT Aptitude Question SOLUTION: 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? (1) –119 (2) –159 (3) –110 (4) -180 (

• Placement Papers
• /
• CAT

CAT Question Papers:

(#M40029239) CAT question CAT quant Keep an EYE

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?
(1) –119
(2) –159
(3) –110
(4) -180
(5) -105

Asked In CAT (11 years ago)

Unsolved Read Solution (1)

Is this Puzzle helpful?   (1)   (3) Submit Your Solution

Read Solution (1) :

Liti  (10 years ago)

ans is 2.

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) = 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 -2x^2 + 4x + 1.
At x = 10, the value is -2 *100 + 4*10 + 1

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.