Differentiation and its Application: The function f defined by f(x)=x^3-3x^2+5x+7 is : | JEE Main 2017

JEE Main 2017 (Online) 9th AprilQuestion 1

The function $f$ defined by $f(x)=x^{3}-3x^{2}+5x+7$ is :

Differentiation and its Application

Decreasing in $R$Increasing in $R$✓ Correct answerIncreasing in $(0,\infty)$ and decreasing in $(-\infty,0)$Decreasing in $(0,\infty)$ and increasing in $(-\infty,0)$

Solution

Concept. Complete the square in $f'$. Formulas used. (1) $f'>0$ everywhere $\Rightarrow$ $f$ increasing on $\mathbb R$Step 1 - Derivative. $f'(x)=3x^2-6x+5=3(x-1)^2+2$. Step 2 - Sign. $f'(x)\ge2>0$ for all $x$, so by (1) $f$ is increasing in $\mathbb R$. Answer: (B)

Differentiation and its Application - JEE Mathematics question (JEE Main 2017 (Online) 9th April)

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