Question
Find the interval of the function that is strictly increasing or decreasing: (x + 1)3 (x - 3)3
✓
Answer
$f(x) = {(x + 1)^3}{(x - 3)^3}$
$f'(x) = {(x + 1)^3}.3{(x - 3)^2} + {(x - 3)^3}.3{(x + 1)^2}$
$ = 3{(x + 1)^2}{(x - 3)^2}[x + 1 + x - 3]$
$ = 3{(x + 1)^2}{(x - 3)^2}[2x - 2]$
$ = 6{(x + 1)^2}{(x - 3)^2}(x - 1)$
Put f'(x) = 0
x = -1, 3, 1
$f'(x) = {(x + 1)^3}.3{(x - 3)^2} + {(x - 3)^3}.3{(x + 1)^2}$
$ = 3{(x + 1)^2}{(x - 3)^2}[x + 1 + x - 3]$
$ = 3{(x + 1)^2}{(x - 3)^2}[2x - 2]$
$ = 6{(x + 1)^2}{(x - 3)^2}(x - 1)$
Put f'(x) = 0
x = -1, 3, 1
| int | Sign of f’(x) | Result |
| $( - \infty , - 1)$ | -ve | Decrease |
| (-1, 1) | -ve | Decrease |
| (1, 3) | +ve | Increase |
| $(3,\infty )$ | +ve | Increase |
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
A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is tan-1(0.5) water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m.
Integrate the function ${e^x}\left( {\frac{{1 + \sin x}}{{1 + \cos x}}} \right)$
→A trust fund has ₹ 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ₹ 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: ₹ 1800
Find the principal value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
→Find the following integrals in Exercises:
$\int\text{x}^2 \bigg(1-\frac{1}{\text{x}^2}\bigg)\text{dx}$
→$\int\text{x}^2 \bigg(1-\frac{1}{\text{x}^2}\bigg)\text{dx}$
If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?
Let $\;f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R$ be defined as f (x) = 3x. Choose the correct answer.
→Define a binary operation on a set.
If the lines $\frac{2 x-1}{4 a}=\frac{y-1}{3}=\frac{2-z}{-1}$ and $\frac{x}{1}=\frac{y}{2 a}=\frac{z}{3}$ are perpendicular to each other, then find the value of a.
→Let A be the set of all 50 students of Class X in a school. Let f : $A \rightarrow N$ be function defined by f(x) = roll number of the student x. Show that f is one-one but not onto.
→