Class 12

Math

Calculus

Application of Derivatives

Find intervals in which the function given by $f(x)=103 x_{4}−54 x_{3}−3x_{2}+536 +11$is (a) strictly increasing (b) strictly decreasing.

$f_{′}(x)=56 x_{3}−512 x_{2}−6x+536 $

If we put $f_{′}(x)=0$

$56 x_{3}−512 x_{2}−6x+536 =0$

$⇒x_{3}−2x_{2}−5x+6=0$

$⇒(x−1)(x+2)(x−3)=0$

$⇒x=1,−2,3$

Now, we will draw these values of $x$ on number line.

Please refer to video to see the number line.

From the number line, we can see that,

For$x∈(−2,1)∪(3,∞),f(x)$ is increasing.

For $x∈(−∞,−2)∪(1,3),f(x)$ is decreasing.