If a function f x x2 bx 1 is increasing in the interval 1 2 then the least value of b is ........

Mathematics (CUET) Previous Year Papers

If a function f(x) = x2 + bx + 1 is increasing in the interval [1, 2], then the least value of b is :

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CUET Mathematics Previous Year Question Paper 2024

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- A function is increasing if its derivative is positive for the interval.

- Here, the derivative of f(x) = x² + bx + 1 is f'(x) = 2x + b.

- For f(x) to be increasing in [1, 2], f'(x) should be greater than or equal to zero in this interval.

- At x = 1, f'(1) = 2(1) + b = 2 + b = 0. This condition implies b = -2.

- At x = 2, f'(2) = 2(2) + b = 4 + b = 0. This condition also implies b = -4.

- The strictest condition for b is b = -2 because it's higher.

- Among the options, -2 is the least value of b that satisfies these conditions.

The correct option is:

- Option 3: -2

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