The function x^5 - 5 x^4 + 5 x^3 - 1 is - Vidyadip

MCQ

The function ${x^5} - 5{x^4} + 5{x^3} - 1$ is

A
Maximum at $x = 3$ and minimum at $x = 1$
B
Minimum at $x = 1$
✓
Neither maximum nor minimum at $x = 0$
D
Maximum at $x = 0$

✓

Answer

Correct option: C.

Neither maximum nor minimum at $x = 0$

c
(c) Let $f(x) = {x^5} - 5{x^4} + 5{x^3} - 1$

==> $f'(x) = 5{x^4} - 20{x^3} + 15{x^2} = 0$

$\therefore (x - 3)(x - 1) = 0$ or $x = 3,1$

Now $f''(x) = 20{x^3} - 60{x^2} + 30x$

Put $x = 3$ and $ 1$ , we get $f'''(3) = + ve$ and $f''(1) = - ve$ and $f''(0) = 0$.

Hence $f(x)$ neither maximum nor minimum at $x = 0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let slope of the tangent line to a curve at any point $P ( x , y )$ be given by $\frac{ xy ^{2}+ y }{ x } .$ If the curve intersects the line $x+2 y=4$ at $x=-2,$ then the value of $y ,$ for which the point $(3, y )$ lies on the curve, is ..... .

The equation of the parabola with focus $(0, 0)$ and directrix $x + y = 4$ is

If $z$ be a complex number satisfying $|\operatorname{Re}(z)|+|\operatorname{Im}(z)|=4,$ then $|z|$ cannot be

If $\overrightarrow x = 3\hat i - 6\hat j - \hat k$ , $\overrightarrow y = \hat i + 4\hat j - 3\hat k$ and $\,\,\overrightarrow z = 3\hat i - 4\hat j - 12\hat k$ , then the magnitude of the projection of $\overrightarrow x \times \overrightarrow y $ on $\overrightarrow z$ is

Let $\mathrm{a}$ and $\mathrm{b}$ be be two distinct positive real numbers. Let $11^{\text {th }}$ term of a $GP$, whose first term is $a$ and third term is $b$, is equal to $p^{\text {th }}$ term of another $GP$, whose first term is $a$ and fifth term is $b$. Then $\mathrm{p}$ is equal to

If $\tan A + \cot A = 4,$ then ${\tan ^4}A + {\cot ^4}A$ is equal to

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. Let $L_{1}: \overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda \overrightarrow{\mathrm{a}}, \lambda \in \mathrm{R}$ and $L_{2}: \vec{r}=(\hat{j}+\hat{k})+\mu \vec{b}, \mu \in R$ be two lines. If the line $L_{3}$ passes through the point of intersection of $L_{1}$ and $L_{2}$, and is parallel to $\vec{a}+\vec{b}$, then $L_{3}$ passes through the point:

$\int_{}^{} {\sqrt {{x^2} - 8x + 7} } \;dx = $

$A = \{1, 2, 3\}$ and $B = \{3, 8\}$, then $(A \cup B) × (A \cap B)$ is

It is $5 : 2$ against a husband who is $65$ years old living till he is $85$ and $4 : 3$ against his wife who is now $58$, living till she is $78$. If the probability that atleast one of them will be alive for $20$ years, is $'k'$, then the value of $'49k'$ -