SOLUTION: Let f be a function such that f(0)=2 and f’ (x)<_6 for -10<_x<_10. 1) what is the maximum possible value of f(2)? 2) can f(5) be negative? Can f(5) equal 0? Why or why not?

Question 1156215: Let f be a function such that f(0)=2 and f’ (x)<_6 for -10<_x<_10.
1) what is the maximum possible value of f(2)?
2) can f(5) be negative? Can f(5) equal 0? Why or why not?

<_ means less than or equal to
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.


1)  The maximum possible value for f(2) under the question is 2 + 6*2 = 2 + 12 = 14.



2)  can f(5) be negative ?    

    ANSWER.  YES.  Take, for example, f(x) = 2 - x. 

                          Then f(0) = 2 and f(5) = 2 - 5 = -3,

                          and f(x) satisfies all imposed conditions.



     can f(5) be equal to 0 ?

     ANSWER.  YES.  Take, for example,  f(x) = 2 - 0.4x.

I answered all the questions.

The function f(x) is assumed to be continue and differentiable in the given interval (in order for the question makes sense).

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