Question 1027572
A) At most, 
{{{(f(4)-f(0))/(4-0)=6}}}
{{{(f(4)-2)/4=6}}}
{{{f(4)-2=24}}}
{{{f(4)=26}}}
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B) At most,
{{{(f(2)-f(0))/(2-0)=6}}}
{{{f(2)-2=12}}}
{{{f(2)=14}}}
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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(0)=2}}}.
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D) {{{f(5)}}} is limited just like {{{f(4)}}} and {{{f(2)}}} are.
The maximum value is,
{{{(f(5)-2)/(5-0)=6}}}
{{{f(5)-2=30}}}
{{{f(5)=32}}}
So, {{{f(5)<=32}}}.