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Mathematics Question on Applications of Determinants and Matrices

The greatest value of f(x)=cos⁡ (xe(x)+7x2−3x),x∈[−1,∞)f(x) = \cos \, (xe^{(x)} + 7x^2 - 3x),x \in [-1, \infty ) is :

A

-1

B

1

C

0

D

none of these

Answer

1

Explanation

Solution

Given : f(x)=cos⁡ (xex+7x2−3x),x∈[−1,∞)f (x) = \cos \, (xe^x + 7x^2 - 3x), x \in [-1, \infty) we know that −1≤ cos⁡θ≤1-1 \le \, \cos \theta \le 1 ∴\therefore greatest value of cos θ\theta is 1 Hence, greatest value of cos⁡ (x.ex+7x2−3x)\cos \, (x.e^x + 7x^2 - 3x) is 1.