MCQ
What are the minimum and maximum values of the function ${x^5} - 5{x^4} + 5{x^3} - 10$
- ✓$-37, -9$
- B$10, 0$
- CIt has $2 $ min. and $1 $ max. values
- DIt has $2$ max. and $ 1$ min. values
$\therefore$ $\frac{{dy}}{{dx}} = 5{x^4} - 20{x^3} + 15{x^2}$$ = \,\,5{x^2}({x^2} - 4x + 3)$
$ = \,\,5{x^2}(x - 3)\,(x - 1)$
$\frac{{dy}}{{dx}} = 0$, gives $x = 0,\,1,\,3$
Now, $\frac{{{d^2}y}}{{d{x^2}}} = 20{x^3} - 60{x^2} + 30x$ = $10x(2{x^2} - 6x + 3)$
and $\frac{{{d^3}y}}{{d{x^3}}} = 10(6{x^2} - 12x + 3)$
For $x = 0$: $\frac{{dy}}{{dx}} = 0,\,\frac{{{d^2}y}}{{d{x^2}}} = 0,\,\frac{{{d^3}y}}{{d{x^3}}} \ne 0$
$\therefore$ Neither minimum nor maximum
For$x = 1,\,\frac{{{d^2}y}}{{d{x^2}}} = - 10 = {\rm{negative}}$.
$\therefore$ Maximum value ${y_{{\rm{max}}{\rm{.}}}} = - 9$
For $x = 3,\,\frac{{{d^2}y}}{{d{x^2}}} = 90 = {\rm{positive}}$
$\therefore$ Minimum value ${y_{{\rm{min}}{\rm{.}}}} = - 37$.
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If A is a singular matrix, then A (adj A) is a
| X: | -4 | -3 | -2 | -1 | 0 |
| P(X): | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
The value of E(X) is: