Question

If the largest interval of $x$ in which the function $f\left(x\right)=x^{3}-3x+1$ is decreasing is $\left(a , b\right)$ , then the value of $a+2b$ is equal to

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

As $f^{'}\left(x\right)=3x^{2}-3=3\left(x - 1\right)\left(x + 1\right)$

i.e. the largest interval in which $f\left(x\right)$ decreases is $\left(- 1,1\right)\Rightarrow a=-1$
$b=1$
$\therefore a+2b=1$