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Higher-order Derivatives

Higher-order Derivatives: Level 2 Challenges


Given the graph of y=f(x)y=f(x) above, which of the following is a possible graph of y=f(x)?y=f''(x)?

Find the 2016-th derivative of sin1(x)\sin ^{ -1 }{ (x) } at x=0x=0.

Give your answer to 3 decimal places.

Image Credit: Flickr Richard Stocker.

If a function f(x)f(x) that is differentiable over (,)(-\infty,\infty) is monotonically decreasing and limxf(x),\displaystyle\lim_{x\rightarrow\infty}f(x)\neq-\infty, then as xx approaches infinity, f(x)f(x) is

y=tan1(x),k!=d21ydx21x=0,     k= ? y = \tan^{-1}(x) , k! = \left. \dfrac { { d }^{ 21 }y }{ d{ x }^{ 21 } } \right|_{x=0}, \ \ \ \ \ k = \ ?

Suppose ff is a function defined on the closed interval 3x4-3 \le x \le 4 with f(0)=42f(0)=42 such that the graph of f,f', the derivative of f,f, on the interval is as shown in the above diagram. Find the xx-coordinates of the points of inflection of f.f.


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