Question #0b94e

Question

3185 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-22T17:50:52

$y(x) = -2x^2 + x + 14$

To arrive at $(dy)/(dx)$ we have differentiated $y(x)$ with respect to $x$ .

To obtain an expression for $y(x)$ we take the anti-derivative or integral of $(dy)/(dx)$ . This comes from the fundamental theorem of calculus.

$y(x) = int (dy)/(dx)dx = int (1-4x)dx = x - 2x^2 + C$

$y(x) = -2x^2 + x + C$

Using the given point we can work out the value of our arbitrary constant:

$y(-2) = 4 = -2(-2)^2 + (-2) + C$

$implies 4 = C - 10 implies C = 14$

$therefore y(x) = -2x^2 + x + 14$