Share

Books Shortlist

# Solution for Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = X4 − 4x ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?

#### Solution

$\text { When } \left( x - a \right)\left( x - b \right)>0 \text { with }a < b, x < a \text { or }x>b.$

$\text { When } \left( x - a \right)\left( x - b \right)<0 \text { with } a < b, a < x < b .$

$f\left( x \right) = x^4 - 4x$

$f'\left( x \right) = 4 x^3 - 4$

$= 4\left( x^3 - 1 \right)$

$\text { For}f(x) \text { to be increasing, we must have }$

$f'\left( x \right) > 0$

$\Rightarrow 4\left( x^3 - 1 \right) > 0$

$\Rightarrow x^3 - 1 > 0$

$\Rightarrow x^3 > 1$

$\Rightarrow x > 1$

$\Rightarrow x \in \left( 1, \infty \right)$

$\text { So,}f(x)\text { is increasing on }\left( 1, \infty \right) .$

$\text { For }f(x) \text { to be decreasing, we must have }$

$f'\left( x \right) < 0$

$\Rightarrow 4\left( x^3 - 1 \right) < 0$

$\Rightarrow x^3 - 1 < 0$

$\Rightarrow x^3 < 1$

$\Rightarrow x < 1$

$\Rightarrow x \in \left( - \infty , 1 \right)$

$\text { So,}f(x)\text { is decreasing on }\left( - \infty , 1 \right).$

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [3]

Solution Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = X4 − 4x ? Concept: Increasing and Decreasing Functions.
S