Question
Find the intervals in which the following functions are increasing or decreasing.
f(x) = 5x3 - 15x2 - 120x + 3.
f(x) = 5x3 - 15x2 - 120x + 3.
✓
Answer
f(x) = 5x3 - 15x2 - 120x + 3 f'(x) = 15x2 - 30x - 120 = 15(x2 - 2x - 8) = 15(x - 4)(x + 2) For f(x) to be increasing, we must have f'(x) > 0 ⇒ 15(x - 4)(x + 2) > 0 ⇒ (x - 4)(x + 2) > 0 [Since, 15 > 0, 15(x - 4)(x + 2) > 0 ⇒ (x - 4)(x + 2) > 0] ⇒ x < -2 or x > 4 $\Rightarrow\text{x}\in(-\infty,-2)\cup(4,\infty)$ So, f(x) is increasing on $\text{x}\in(-\infty,-2)\cap(4,\infty).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the value of k if f(x) is continuous at $\text{x}=\frac{\pi}{2},$ where
$\text{f}\text{(x)}=\begin{cases}\frac{\text{k}\cos\text{x}}{\pi-2\text{x}}, &\text{ x}\neq\frac{\pi}{2}\\3, &\text{ x}=\frac{\pi}{2}\end{cases}$
→$\text{f}\text{(x)}=\begin{cases}\frac{\text{k}\cos\text{x}}{\pi-2\text{x}}, &\text{ x}\neq\frac{\pi}{2}\\3, &\text{ x}=\frac{\pi}{2}\end{cases}$
Solve the following differential equation:
$(\text{x}+\tan\text{y})\text{dy}=\sin2\text{y dx}$
→$(\text{x}+\tan\text{y})\text{dy}=\sin2\text{y dx}$
Find the angle between the vectors whose direction cosines are proportional to 2, 3, -6 and 3, -4, 5.
In the following, determine the values of constants involved in the definition so that the given function is continuous:
$\text{f(x)}=\begin{cases}4,&\text{if }\text{ x}\leq-1\\\text{ax}^2+\text{b},&\text{if }-1<\text{ x}<0\\\cos\text{x},&\text{if }\text{ x}\geq0\end{cases}$
→$\text{f(x)}=\begin{cases}4,&\text{if }\text{ x}\leq-1\\\text{ax}^2+\text{b},&\text{if }-1<\text{ x}<0\\\cos\text{x},&\text{if }\text{ x}\geq0\end{cases}$
Minimize Z = 3x + 2y subject to the constraints:
$x + y \geq 8$
$3 x + 5 y \leq 15$
$x \geq 0 , \ y \geq 0$
→$x + y \geq 8$
$3 x + 5 y \leq 15$
$x \geq 0 , \ y \geq 0$
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\sin\text{x}|\sin\text{x}|\text{dx}$
→$\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\sin\text{x}|\sin\text{x}|\text{dx}$
If $\text{y}=\text{x}^3\log\text{x},$ Prove that $\frac{\text{d}^4\text{y}}{\text{dx}^4}=\frac{6}{\text{x}}$
→A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
Solve the following differential equation:
$(\text{x}-\text{y})\frac{\text{dy}}{\text{dx}}=\text{x + 2y}$
→$(\text{x}-\text{y})\frac{\text{dy}}{\text{dx}}=\text{x + 2y}$
Find the matrix A satisfying the matrix equation:
→$\begin{bmatrix}2&1\\3&2\end{bmatrix}\text{A}\begin{bmatrix}-3&2\\5&-3\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}.$