If f(x) = 2x^6 - 3,then: | vedclass

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

Question

(C) To find the local extrema of the function $f(x) = 2x^6 - 3$,we first find its derivative.$f'(x) = \frac{d}{dx}(2x^6 - 3) = 12x^5$.Setting the deri

Vedclass · Accepted Answer

$-3$ is the local minimum value of $f$

Vedclass · Answer

(C) To find the local extrema of the function $f(x) = 2x^6 - 3$,we first find its derivative.$f'(x) = \frac{d}{dx}(2x^6 - 3) = 12x^5$.Setting the derivative equal to zero to find critical points:$12x^5 = 0 \implies x = 0$.Now,we use the first derivative test or second derivative test to check the nature of the point $x = 0$.Using the first derivative test:For $x For $x > 0$,$f'(x) = 12x^5 > 0$ (function is increasing).Since the derivative changes sign from negative to positive at $x = 0$,the function has a local minimum at $x = 0$.The local minimum value is $f(0) = 2(0)^6 - 3 = -3$.Thus,$-3$ is the local minimum value of $f$.

If $f(x) = 2x^6 - 3$,then:

Similar Questions

If $x + y = 16$ and $x^2 + y^2$ is minimum,then the values of $x$ and $y$ are

$A$ ball is thrown in the air. Its height at any time $t$ is given by $h = 3 + 14t - 5t^2$. What is the maximum height it can reach?

The function $f(x) = x^5 - 5x^4 + 5x^3 - 1$ is:

The maximum value of the function $f(x) = \frac{\log x}{x}, x > 0$ is

Consider a square of side $2 \ cm$. It is cut from one of its corners as shown in the adjacent figure. The maximum value of the sum of the perimeters of the two plane figures thus formed is

Vedclass Test Series

Exam Paper Generator

Online Exam Module