Question

The function $x^5-5x^4+5x^3-10$ has a maximum where $x=$

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is C

$1$

Step 1: Explanation for the correct option

Option$\left(c\right)$: By substituting the $x=1$in given function we get,

$$\begin{gathered} f\left(1\right)=1^5-5\times 1^4+5\times 1^3-10 \\ =1-5+5-10 \\ =9 \end{gathered}$$

As the function have a maximum value at $x=1$

Therefore, option $\left(c\right)$ is correct.

Step 2: Explanation for the incorrect options

Option$\left(a\right)$: By substituting the $x=3$ in given function we get,

$$\begin{gathered} f\left(3\right)=3^5-5\times 3^4+5\times 3^3-10 \\ =243-405+135-10 \\ =-37 \end{gathered}$$

Therefore, option $\left(a\right)$is incorrect.

Option$\left(b\right)$: By substituting the $x=2$ in given function we get,

$$\begin{gathered} f\left(2\right)=2^5-5\times 2^4+5\times 2^3-10 \\ =32-80+40-10 \\ =-18 \end{gathered}$$

Therefore, option $\left(b\right)$is incorrect.

Option$\left(d\right)$: By substituting the $x=0$ in given function we get,

$$\begin{gathered} f\left(0\right)=0^5-5\times 0^4+5\times 0^3-10 \\ =0-0+0-10 \\ =-10 \end{gathered}$$

Therefore, option $\left(d\right)$is incorrect.

Hence, the correct answer is option $\left(c\right)$ $1$.