CAT 2025 Linear and Quadratic Equations Question (Hard)

Question

A value of c for which the minimum value of f x x 2-4 c x 8 c is greater than the maximum value of g x -x 2 3 c x-2 c , is

Accepted Answer

First function f left x right x 2-4cx 8 For this function a 0, so minimum value will occur at x - 2a - left - 2 right 2c So, the minimum value of the function is 2c 2-4c left 2c right 8c -4c 2 8c Second function g x -x 2 3cx-2c For this function a 0, so maximum value will occur at x - 2a - 2 2 So, t

CAT 2025

Quantitative

Linear and Quadratic Equations

Hard

A value of (c) for which the minimum value of (f(x)=x^2-4 c x+8 c) is greater than the maximum value of (g(x)=-x^2+3 c x-2 c), is

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