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# Solution for Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = X8 + 6x2 ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Find the interval in which the following function are increasing or decreasing f(x) = x8 + 6x2  ?

#### Solution

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

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

$f\left( x \right) = x^8 + 6 x^2$

$f'\left( x \right) = 8 x^7 + 12x$

$= 4x \left( 2 x^6 + 3 \right)$

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

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

$\Rightarrow 4x \left( 2 x^6 + 3 \right) > 0 \left[ \text { Since } \left( 2 x^6 + 3 \right) > 0, 4x \left( 2 x^6 + 3 \right) > 0 \Rightarrow x > 0 \right]$

$\Rightarrow x > 0$

$\Rightarrow x \in \left( 0, \infty \right)$

$\text { So ,f(x)is increasing on x }\in \left( 0, \infty \right) .$

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

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

$\Rightarrow 4x \left( 2 x^6 + 3 \right) < 0$

$\Rightarrow x < 0 \left[ \text { Since } \left( 2 x^6 + 3 \right) > 0, 4x \left( 2 x^6 + 3 \right) < 0 \Rightarrow x < 0 \right]$

$\Rightarrow x \in \left( - \infty , 0 \right)$

$\text { So,f(x)is decreasing on x }\in \left( - \infty , 0 \right) .$

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Solution Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = X8 + 6x2 ? Concept: Increasing and Decreasing Functions.
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