Please help this is timed For which function and interval can the extreme value theorem be applied?
f(x) =х/(x-6)^2 over the interval [3, 5] f(x) = -5/2(x-7)^3 over the interval (6, 8)
f(x) = 4 tan(πX) over the interval [0, 1]
f(x) = 3e^x + 1 over the interval (1, 3)

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.