The interval in which the function, f(x)

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The interval in which the function, f(x) = 7 – 4x – x² is strictly increasing is

Options:

(-∞, ∞)

(–2, ∞)

(-∞, -2)

Correct Answer:

(-∞, -2)

Explanation:

$f(x) = 7 - 4x - x^2$

$f'(x) > 0$

$f'(x)=\frac{d}{dx}(7 - 4x - x^2)$

{$\frac{d}{dx}x^n=nx^{n-1}$} $\frac{d}{dx}(c)=0$

$= 0-4-2x⇒-(4+2x)$

$-(4+2x)>0$

$4+2x<0⇒2x<-4$

$x<-2$

$x∈(-∞, -2) $