Question

Question #0b94e

Answer 1

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

Explanation:

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`