Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 143: 101

$a$ = $-\frac{1}{2}$ $b$ = $2$

$y$ = $f(x)$ = $ax^{2}$ $f'(x)$ = $2ax$ slope of the tangent to the parabola at $x$ = $2$ $m$ = $2ax$ = $2a(2)$ = $4a$ slope of the given line is $2x+y$ = $b$ $y$ = $-2x+b$ $m$ = $-2$ $4a$ = $-2$ $a$ = $-\frac{1}{2}$ when $x$ = $2$ $y$ = $-\frac{1}{2}(2)^{2}$ = $-2$ so $2x+y$ = $b$ $2(2)-2$ = $b$ $b$ = $2$