Calculus

Application of Derivatives

Easy

core

In which of the following intervals, the function $f(x) = -x^2 - 2x + 15$ is decreasing?

$(-1, \infty)$

$(-\infty, -1)$

$(-\infty, 2)$

$(0, -1)$

✅ Correct Option: 1

Given: $f(x) = -x^2 - 2x + 15$

A function is decreasing where its derivative is negative.

Using the power rule:

$f'(x) = -2x - 2$

For the function to be decreasing:

$f'(x) < 0$

$-2x - 2 < 0$

$-2x < 2$

Dividing both sides by $-2$ (inequality sign flips when dividing by a negative number):

$x > -1$

In interval notation: $(-1, \infty)$

Therefore, the function $f(x) = -x^2 - 2x + 15$ is decreasing on the interval $(-1, \infty)$ .

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C. increasing in $(-\infty, 0)$

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B. Point of local minima is	II. -83
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The function $f(x) = \frac{4x^2+1}{x}$ is decreasing in

(A). $\left(\frac{-1}{2}, \frac{1}{2}\right)$

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(C). $\left(0, \frac{1}{2}\right)$

(D). $\left(\frac{-1}{2}, 0\right)$

Choose the correct answer from the options given below:

In which of the following intervals, the function f(x)=−x2−2x+15f(x) = -x^2 - 2x + 15f(x)=−x2−2x+15 is decreasing?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

In which of the following intervals, the function $f(x) = -x^2 - 2x + 15$ is decreasing?