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?
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?
Option 1 -
-119
Option 2 -
-159
Option 3 -
-110
Option 4 -
-180
Asked by Shiksha User
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1 Answer
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Correct Option - 2
Detailed Solution:Let f (x) = px2 + qx + k, where p, q and k are integers, and p ≠ 0
f (0) = k = 1
f (x) = px2 + qx + 1
= px2 +qx + k (Differentiate both sides with respect to x)
f' (x) = 2px + q
For maxima or minima f' (x) = 0, x =
f (x) attains maximum at x = 1
q = − 2p
f (1) = p + q + 1 = 3
1 − p = 3
p = − 2
q = 4
f (x) = −2x2 + 4x + 1
f (10) = − 200 + 40 + 1 = −159
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