SOLUTION: Let f be a function such that f(0) = 2 and f'(x)<=6 for -10<=x<=10. A) What is the maximum possible value of f(4)? B) What is the maximum possible value of f(2)? C) Can f(5) be

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Let f be a function such that f(0) = 2 and f'(x)<=6 for -10<=x<=10. A) What is the maximum possible value of f(4)? B) What is the maximum possible value of f(2)? C) Can f(5) be       Log On


   

Question 1027572: Let f be a function such that f(0) = 2 and f'(x)<=6 for -10<=x<=10.
A) What is the maximum possible value of f(4)?
B) What is the maximum possible value of f(2)?
C) Can f(5) be negative? Can f(5) = 0? Why or Why not?
D) Can f(5) = 31? Can f(5) = 35? Why or why not?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A) At most,
%28f%284%29-f%280%29%29%2F%284-0%29=6
%28f%284%29-2%29%2F4=6
f%284%29-2=24
f%284%29=26
.
.
B) At most,
%28f%282%29-f%280%29%29%2F%282-0%29=6
f%282%29-2=12
f%282%29=14
.
.
C) Yes, the only limit is on the positive end. The derivative can be negative so then the value can take any value less than f%280%29=2.
.
.
.
D) f%285%29 is limited just like f%284%29 and f%282%29 are.
The maximum value is,
%28f%285%29-2%29%2F%285-0%29=6
f%285%29-2=30
f%285%29=32
So, f%285%29%3C=32.