The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range

For the integral $\rm I=\displaystyle\int^1_{-1}\frac{1}{x^2}dx$

which of the following statements is TRUE? 

The following function is defined over the interval [-L, L]:

f(x) = px4 + qx5.

If it is expressed as a Fourier series, 

$\rm f(x)=a_0 +\displaystyle\sum^\infty_{n=1} \left\{a_n \sin\left( \frac{\pi x}{L} \right) +b_n\cos\left( \frac{\pi x}{L} \right) \right\} $,

which options amongst the following are true?

Consider the polynomial f(x) = x³ $$-$$ 6x² + 11x $$-$$ 6 on the domain S, given by 1 $$\le$$ x $$\le$$ 3. The first and second derivatives are f'(x) and f''(x).

Consider the following statements :

I. The given polynomial is zero at the boundary points x = 1 and x = 3.

II. There exists one local maxima of f(x) within the domain S.

III. The second derivative f''(x) > 0 throughout the domains S.

IV. There exists one local minima f(x) within the domain S.