Consider the function f(x)=2x^(3) −6x^(2) −48x+7 By the Mean Value Theorem, we know there exists at least one value c in the open interval (−4,8) such that f′(c) is equal to this mean slope. List all values c that work.

answer: was that a question or answer?

step-by-step explanation:

i believe the answer is the polygon, heptagon.

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.

$450 i think. hope this ☺