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.

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(52795) (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.
~~~~~~~~~~~~~~~~~~~

Since f'(x) = ax+1, we have  f(x) = ,  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

     = -3,

or

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


ANSWER.  f(x) = .

Solved.

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