What is the minimum value of 2^{((x^2 - 3)^3 | vedclass

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

Question

(C) The expression $2^{((x^2 - 3)^3 + 27)}$ attains its minimum value when the exponent $((x^2 - 3)^3 + 27)$ is minimized.Let $f(x) = (x^2 - 3)^3 + 27

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) The expression $2^{((x^2 - 3)^3 + 27)}$ attains its minimum value when the exponent $((x^2 - 3)^3 + 27)$ is minimized.Let $f(x) = (x^2 - 3)^3 + 27$.To find the minimum,we analyze the behavior of $(x^2 - 3)^3$.The term $(x^2 - 3)^3$ can take any real value because the range of $x^2 - 3$ is $[-3, \infty)$,and the cube function is strictly increasing.However,if we consider the domain of $x$ as all real numbers,$(x^2 - 3)^3$ can approach $-\infty$ as $x^2$ approaches $0$ (specifically,$(-3)^3 = -27$).Thus,the minimum value of $(x^2 - 3)^3 + 27$ is $(-27) + 27 = 0$.Therefore,the minimum value of the expression is $2^0 = 1$.

What is the minimum value of $2^{((x^2 - 3)^3 + 27)}$?

Similar Questions

If $A+C=2B$,then $\frac{\cos C-\cos A}{\sin A-\sin C}$ is equal to

For $a \in R - \{0\}$,if $a \cos x + a \sin x + a = 2K + 1$ has a solution,then $K$ lies in the interval

The maximum value of the function $f(x) = a \sin x + b \cos x$ is:

The value of $\sin \theta + \cos \theta$ will be greatest when

What is the maximum value of the function $f(x) = \sin x + \cos x$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module