f: `D->R, f(x) = (x^2 +bx+c)/(x^2+b_1 x+c_1)` where`alpha,beta` are the roots of the equation `x^2+bx+c=0` and `alpha_1,beta_1` are the roots of `x^2+b_1 x+ c_1= 0`. Now answer the following questions for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. (If `alpha_1 and beta_1` are real, then f(x) has vertical asymptote at x = `(alpha_1,beta_1)`
If `alpha_1 lt alpha lt beta_1 lt beta`, then

Options

A. f(x) has a maxima in `[alpha_(1),beta_(1)]` and a minima is `[alpha,beta]`
B. f(x) has a minima in `(alpha_(1),beta_(1))` and a maxima in `(alpha,beta)`
C. `f'(x)gt0` where ever defined
D. `f'(x)lt0` where ever defined

Answer

A