Higher-order Derivatives

Higher-order Derivatives: Level 1 Challenges


What is the fewest number of derivatives one needs to compute so that f(x)=568x499f(x) = 568{ x }^{ 499 } becomes zero?

In the above diagram, the red curve is the graph of a function f,f, and the blue curve is the graph of its first derivative f.f'. What is the relationship between f(1)f'(-1) and f(1)?f''(1) ?

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)?

Let PP be a point moving in the xyxy-plane whose coordinates at time tt are given by x(t)=2etsint,y(t)=6cost.x(t)=2e^t\sin t, y(t)=6\cos t. What is the minimum value of the magnitude of the acceleration of P?P?

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

f(x)=sinx+x100000\large{ f(x) = \sin x + x^{100000}}

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


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