Math Problem Statement

Найти экстремумы функции:1)f (x) =x3-6x2+9x-4

Solution

Для нахождения экстремумов функции f(x)=x3−6x2+9x−4f(x) = x^3 - 6x^2 + 9x - 4, нужно пройти несколько этапов.

Шаг 1. Найти первую производную функции

Для начала вычислим первую производную функции:

f′(x)=ddx(x3−6x2+9x−4)f'(x) = \frac{d}{dx} \left( x^3 - 6x^2 + 9x - 4 \right)

Используем стандартные правила дифференцирования:

[ f'(x)

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Extrema
Critical Points

Formulas

First derivative f'(x) = d/dx (x^3 - 6x^2 + 9x - 4)

Theorems

First derivative test
Critical point theorem

Suitable Grade Level

Grades 11-12

Related Recommendation

Find Extrema and Intervals of Increase/Decrease for x^3 - 6x^2 + 9x - 4

Absolute Maximum and Minimum of f(x) = 2x^3 - x^2 - 4x + 6

First Derivative Test to Find Maxima and Minima of f(x) = x^3 - 9x^2 + 24x

Find Absolute Maximum and Minimum of Cubic Function on Interval [-1, 0]

Find Critical Points of the Function f(x) = x^3 + 6x^2 - 3x + 4