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Solution for Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = 10 − 6x − 2x2 ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

Question

Find the interval in which the following function are increasing or decreasing f(x) = 10 − 6x − 2x2  ?

Solution

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

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

$f(x) = 10 - 6x - 2 x^2$

$f'(x) = - 6 - 4x$

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

$f'(x) > 0$

$\Rightarrow - 6 - 4x > 0$

$\Rightarrow - 4x > 6$

$\Rightarrow x < \frac{- 3}{2}$

$\Rightarrow x \in \left( - \infty , \frac{- 3}{2} \right)$

$\text { So }, f(x) \text { is increasing on } \left( - \infty , \frac{- 3}{2} \right) .$

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

$f'(x) < 0$

$\Rightarrow - 6 - 4x < 0$

$\Rightarrow - 4x < 6$

$\Rightarrow x > \frac{- 6}{4}$

$\Rightarrow x > \frac{- 3}{2}$

$\Rightarrow x \in \left( \frac{- 3}{2}, \infty \right)$

$\text { So }, f(x) \text { is decreasing on } \left( \frac{- 3}{2}, \infty \right) .$

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Solution Find the Interval in Which the Following Function Are Increasing Or Decreasing F(X) = 10 − 6x − 2x2 ? Concept: Increasing and Decreasing Functions.
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