The function y = 2x^3 - 9x^2 + 12x - 6 is mon | vedclass

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

Question

(A) Given the function $f(x) = 2x^3 - 9x^2 + 12x - 6$. First,we find the derivative of the function with respect to $x$: $f'(x) = \frac{d}{dx}(2x^3 -

Vedclass · Accepted Answer

$1 < x < 2$

Vedclass · Answer

(A) Given the function $f(x) = 2x^3 - 9x^2 + 12x - 6$. First,we find the derivative of the function with respect to $x$: $f'(x) = \frac{d}{dx}(2x^3 - 9x^2 + 12x - 6) = 6x^2 - 18x + 12$. For the function to be monotonically decreasing,we must have $f'(x) $6x^2 - 18x + 12 Dividing the inequality by $6$,we get: $x^2 - 3x + 2 Factoring the quadratic expression: $(x - 1)(x - 2) This inequality holds when $x$ lies between the roots $1$ and $2$. Therefore,the function is monotonically decreasing for $1 < x < 2$.

The function $y = 2x^3 - 9x^2 + 12x - 6$ is monotonically decreasing when

Similar Questions

If $f(x) = \sin x - \cos x$,$0 \leq x \leq 2\pi$,then $f(x)$ is strictly decreasing in the interval:

Let $f: [0, 2] \to R$ be a twice differentiable function such that $f''(x) > 0$ for all $x \in (0, 2)$. If $\phi(x) = f(x) + f(2 - x)$,then $\phi$ is

In which interval is the function $f(x) = x^2 - x + 1$ not monotonic?

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

The function $f(x) = \tan x - x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module