The gradient of a curve at any point (x y) is 7-2x.Given that the curve passes through(3,2) find the equation of the curve?

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Answer 1 · 2017-08-27T14:59:09

The curve has equation #-x^2 + 7x - 10#

We can deduce that the derivative of the function is

#f'(x) = 7 - 2x#

Using the basic anti-derivative rules, we obtain that

#f(x) = 7x - x^2 + C#

To find #C#, we must plug in the point #(3, 2)#.

#2 = 7(3) - 3^2 + C#

#2 - 21 + 9 = C#

#-10 = C#

The equation of the curve is therefore #f(x) = 7x -x^2 - 10#

Hopefully this helps!