The function f: R R is defined by f(x) = x - (x3)/(3). Find the monotony of f, showing clearly its variation table.

May 24, 2026Mathematics

ScanSolve AI Answer

May 24, 2026

Answer

x - \frac{x^3}{3}$$

Here are the solutions to the remaining questions.

Question 3:

i) The function $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = x - \frac{x^3}{3}$ . Find the monotony of $f$ , showing clearly its variation table.

Step 1: Find the first derivative of $f(x)$ . $f(x) = x - \frac{x^3}{3}$ $f'(x) = \frac{d}{dx}\left(x - \frac{x^3}{3}\right) = 1 - \frac{3x^2}{3} = 1 - x^2$

Step 2: Find the critical

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QTell me about algebra please Qयदि sec A = cosec B = 13/12 तब (A + B) का मान है QSolve: 2x2 - 5x + 3 = 0 Qदो मीनारों के शीषों को इन मीनारों वाली रेखा के मध्य बिन्दु से देखने पर उनके उन्नयन कोण क्रमशः 60° तथ…QA sector of 270° is removed from a thin circular sheet of metal. The remaining area is then folded t…

See all Mathematics questions →

Still have questions?

Quick Answer

i) The function f: R R is defined by f(x) = x - (x^3)/(3). Find the monotony of f, showing clearly its variation table.

Asked on May 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 24, 2026

Here are the solutions to the remaining questions. Question 3: i) The function f: R R is defined by f(x) = x - (x^3)/(3). Find the monotony of f, showing clearly its variation table. Step 1: Find the first derivative of f(x). f(x) = x - (x^3)/(3) f'(x) = (d)/(dx)(x - (x^3)/(3)) = 1 - (3x^2)/(3) = 1 - x^2 Step 2: Find the critical