Question #0b94e

1 Answer
Aug 22, 2016

#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#