Mrs. Jackson gives the table below to her students. In order for the function to be linear, what must a be and why? a = 22 becau
se the rate of change is 1. a = 20 because the rate of change is 3. a = 22 because the rate of change is –1. a = 20 because the rate of change is –3.
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If you know the derivative of some function
, you can tell exactly who
is, up to an additive, constant term. In fact, knowing
, you have
In your case, we have
So, the integral is almost immediate:
So, up to some constant additive term, our function is
To fix this constant, we know that the function passes through the point (6,10), so we have
And so our function is
If we want to know when this function equals 6, we simply have to ask and solve for x, so we have