SOLUTION: 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.

Algebra ->  Functions -> SOLUTION: 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.       Log On


   

Question 1192678: 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.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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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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Since f'(x) = ax+1, we have  f(x) = %28a%2F2%29%2Ax%5E2+%2B+x+%2B+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

    %28a%2F2%29%2A3%5E2+%2B+3+%2B+3 = -3,

or

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


ANSWER.  f(x) = -x%5E2+%2B+x+%2B+3.

Solved.