For what values of x is the function f(x) = x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the function $f(x) = x^3 - 3x^2 - 9x + 22$. To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x

Vedclass · Accepted Answer

$-1 < x < 3$

Vedclass · Answer

(A) Given the function $f(x) = x^3 - 3x^2 - 9x + 22$. To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x)$. $f'(x) = \frac{d}{dx}(x^3 - 3x^2 - 9x + 22) = 3x^2 - 6x - 9$. For the function to be strictly decreasing,$f'(x) $3x^2 - 6x - 9 Dividing by $3$,we get $x^2 - 2x - 3 Factoring the quadratic expression: $(x - 3)(x + 1) The roots of the equation $(x - 3)(x + 1) = 0$ are $x = 3$ and $x = -1$. Testing the intervals $(-\infty, -1)$,$(-1, 3)$,and $(3, \infty)$,we find that the expression is negative in the interval $(-1, 3)$. Therefore,the function is strictly decreasing for $-1 < x < 3$.

For what values of $x$ is the function $f(x) = x^3 - 3x^2 - 9x + 22$ strictly decreasing?

Similar Questions

Let $f(x) = \int {e^x}(x - 1)(x - 2)dx$. Then $f$ decreases in the interval

Let $f(x) = \int e^x (x - 1)(x - 2) dx$. In which interval is $f$ a decreasing function?

If a function $f(x)$ is increasing in an interval $x \in [a, b]$,then which of the following will always be correct?

The function $f(x) = (x - 2)|x - 3|$ is monotonically increasing in:

Let $f:(-1, \infty) \rightarrow \mathbb{R}$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x} \ln(1+x), x \neq 0$. Then the function $f$

Vedclass Test Series

Exam Paper Generator

Online Exam Module