Question 1192678
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A curve has gradient function f'(x) = ax+1 where a is constant. 
Find f(x) given that f(0) = 3 and f(3) = -3.
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<pre>
Since f'(x) = ax+1, we have  f(x) = {{{(a/2)*x^2 + x + c}}},  where c is a constant term.


Since f(0) = 3 (given), it implies  c= 3.


To determine value of "a", use the condition f(3) = -3.  It gives you an equation

    {{{(a/2)*3^2 + 3 + 3}}} = -3,

or

    9a/2 = - 9,  i.e.  a = -2.


<U>ANSWER</U>.  f(x) = {{{-x^2 + x + 3}}}.
</pre>

Solved.