Given the equation ƒ(a) = a

^{2} - a + 6, determine the 2nd derivative ƒ''(a)

Using the power rule, the derivative ƒ'(a) of aa

^{n} = (a * n)a

^{(n - 1)} For this term, a = 1, n = 2, and a is the variable we derive in terms of

ƒ(a) = a

^{2} ƒ'(a) = (1 * 2)a

^{(2 - 1)}ƒ'(a) = 2a <--- Used in our final answer.

Using the power rule, the derivative ƒ'(a) of aa

^{n} = (a * n)a

^{(n - 1)} For this term, a = -1, n = 1, and a is the variable we derive in terms of

ƒ(a) = -a

ƒ'(a) = (-1 * 1)a

^{(1 - 1)}ƒ'(a) = -1 <--- Used in our final answer.

__Collecting all of our derivative terms we get:__ ƒ'(a) =

**2a - 1**### Now start 2nd derivative ƒ''(a) of our first derivative above

Using the power rule, the derivative ƒ''(a) of aa

^{n} = (a * n)a

^{(n - 1)} For this term, a = 2, n = 1, and a is the variable we derive in terms of

ƒ'(a) = 2a

ƒ''(a) = (2 * 1)a

^{(1 - 1)}ƒ''(a) = 2 <--- Used in our final answer.

Using the power rule, the derivative ƒ''(a) of aa

^{n} = (a * n)a

^{(n - 1)} For this term, a = -1, n = 0, and a is the variable we derive in terms of

ƒ'(a) = -1

ƒ''(a) = 0 <--- The derivative of a constant = 0. This is part of our answer.

__Collecting all of our derivative terms we get:__ ƒ''(a) =

**2**__Evaluate ƒ''(0)__ƒ''(0) = 2

ƒ''(0) = 2

ƒ''(0) = 2

ƒ''(0) =

**2**