Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = x^3 - 6x^2 - 36x + 2$

✓

Answer

$f(x) = x^3 - 6x^2 - 36x + 2$
$\therefore f'(x) = 3x^2 - 12x - 36$
Critical point
$f'(x) = 0$
$\Rightarrow 3(x^2 - 4x - 12) = 0$
$\Rightarrow (x - 6)(x + 2) = 0$
$\Rightarrow x = 6, -2$
Clearly, $f'(x) > 0$ if $x < -2$ and $x > 6$
$f'(x) < 0$ if $-2x < x < 6$
Thus, f(x) increases in $(-\infty,-2)\cup(6,\infty),$ decreases in $(-2, 6).$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find $\int \frac{x^2-3 x+1}{\sqrt{1-x^2}} d x$

Find $f^{-1}$ if it exists: $f: A \rightarrow B$, where, $A=\{1,3,5,7,9\} ; B=\{0,1,9,25,49,81\}$ and $f(x)=x^2$.

Using vector method prove that in any triangle ABC,
$
\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} .
$

If P(A) = 0.4, P(B) = 0.3 and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.5$ find $\text{P}(\text{A}\cap\text{B})$ and $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big).$

Evaluate the following integrals:
$\int^\limits4_1\text{f(x)}\text{dx},$ Where $\text{f(x)}=\begin{cases}7\text{x}+3,&\text{if }\ 1\leq\text{x}\leq3\\8\text{x},&\text{if }\ 3\leq\text{x}\leq9\end{cases}$

The radius of the circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Evaluate the following integrals:
$\int\text{e}^\text{x}\sqrt{\text{e}^{2\text{x}}+1}\text{dx}$

Find the equation of the plane with intercept 3 on the y-axis and parallel to the ZOX plane.

Find A (adjoint A) for the matrix $\text{A}=\begin{bmatrix}1 & -2 & 3 \\0 & 2 & -1 \\ -4 & 5 & 2 \end{bmatrix}$.

Prove that the greatest integer function defined by
$\text{f(x)} = [\text{x} ], 0 < \text{x} < 3$
is not differentiable at x = 1 and x = 2.