For the function f(x)=x^3-6x^2-12x-3,x=2 is a | vedclass

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

Question

(C) Given the function $f(x) = x^3 - 6x^2 - 12x - 3$. First,find the first derivative: $f'(x) = 3x^2 - 12x - 12$. Next,find the second derivative: $f'

Vedclass · Accepted Answer

point of inflection

Vedclass · Answer

(C) Given the function $f(x) = x^3 - 6x^2 - 12x - 3$. First,find the first derivative: $f'(x) = 3x^2 - 12x - 12$. Next,find the second derivative: $f''(x) = 6x - 12$. Evaluate the second derivative at $x = 2$: $f''(2) = 6(2) - 12 = 12 - 12 = 0$. Since $f'(2) = 3(2)^2 - 12(2) - 12 = 12 - 24 - 12 = -24 
eq 0$,$x=2$ is not a critical point. However,checking the options provided,the question implies evaluating the nature of the point where $f''(x)=0$. Since $f''(x)$ changes sign at $x=2$ (for $x  2$,$f''(x) > 0$),$x=2$ is a point of inflection.

For the function $f(x)=x^3-6x^2-12x-3$,$x=2$ is a

Similar Questions

For a steamer,the consumption of petrol (per hour) varies as the cube of its speed (in $km/hr$). If the speed of the current is steady at $C \, km/hr$,then the most economical speed of the steamer going against the current will be ........... $C$.

Find two numbers whose sum is $24$ and whose product is as large as possible.

Maximum value of $x(1 - x)^2$ when $0 \le x \le 2$,is

Local maximum and local minimum values of the function $f(x) = (x - 1)(x + 2)^2$ are

Among all sectors of a fixed perimeter,choose the one with maximum area. Then,the angle at the centre of this sector (i.e.,the angle between the bounding radii) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module