Posted by Anonymous on Sunday, November 18, 2007 at 12:49am.
The slope of a curve is at the point (x,y) is 4x-3. Find the curve if it is required to pass through the point (1,1).
calculus - Reiny, Sunday, November 18, 2007 at 1:26am
4x - 3 is your slope, so it is the derivative.
then dy/dx = 4x + 3, integrate to get
y = 2x^2 + 3x + k
plug in (1,1) into that to get k, and you are done!
calculus - Anonymous, Sunday, November 18, 2007 at 11:43am
why would I solve for the constant? I get k=-4. What is meant by curve?
calculus - Reiny, Sunday, November 18, 2007 at 3:01pm
When they say "find the curve" they mean find the equation of function whose graph would be that curve.
your equation y = 2x^2 + 3x - 4 would graph to be a parabola, and a parabola is a curve.
As to the constant, remember that if you differentiate an equation like
y = 2x^2 + 3x - 4
you get y' = 4x + 3 - 0
so when we "anti-differentiate" that we really don't know what the value of the constant was, because its derivative would be zero no matter what the number was.
That is why we include a constant value of c or k to allow for that. Once we sub in the given point we then know the value of that constant
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