Question

$f\left(x\right)$ is cubic polynomial which has local maximum at $x=-1$. If $f\left(2\right)=18,f\left(1\right)=-1$ and $f\left(x\right)$ has local minima at $x=0$, then

• A. the distance between $(-1,2)$ and $(a,f(a\left)\right)$, where $x=a$ is the point of local minima is 2 $\sqrt{5}$
• B. $f\left(x\right)$ is increasing for $x\in [1,2\sqrt{5}]$
• C. $f\left(x\right)$ has local minima at $x=1$
• D. the value of $f\left(0\right)=5$

Answer 1

Answer: (B), (C)

The correct options are
B $f\left(x\right)$ is increasing for $x\in [1,2\sqrt{5}]$
C $f\left(x\right)$ has local minima at $x=1$

The required polynomial which satisfy the condition
$isf\left(x\right)=\frac{1}{4}(19x^3-57x+34)$
$f\left(x\right)$ has local maximum at $x=-1$ and local
minimum at $x=1$
Hence $f\left(x\right)$ is increasing for $x\in [1,2\sqrt{5}]$.