Calculus
# Higher-order Derivatives

$f,$ and the blue curve is the graph of its first derivative $f'.$ What is the relationship between $f'(-1)$ and $f''(1) ?$

In the above diagram, the red curve is the graph of a function$y=f(x)$ above, which of the following is a possible graph of $y=f''(x)?$

Given the graph of

Find $f^{(100)}(0)$. If

$\large{ f(x) = \sin x + x^{100000}}$

**Note:** $f^n(x)$ denotes the $n^{th}$ derivative of $f(x)$.