# Math Help - differentiation question

1. ## differentiation question

For what values of a and b is the line 2x+y=b tangent to the parabola y=ax^2 when x=2

2. Originally Posted by cityismine
For what values of a and b is the line 2x+y=b tangent to the parabola y=ax^2 when x=2

When $x = 2, y = 4a$.

$y' = 2ax = 4a$

$y - 4a = y'(x - 2) = 4a(x - 2) \Rightarrow y - 4a = 4ax - 8a \Rightarrow y = 4ax - 4a$

Comparing $y = 4ax - 4a$ and $2x + y = b$,

Writing it: $-4a = -4ax + y$ makes it easy.

$2 = -4a = b \Rightarrow a = -\frac{1}{2} , b = 2$