Problem Bank | IB Math AAHL

[Maximum mark: 24]

Consider the function f(x)=exx2, x∈R.

Let f(n) denote the nth derivative of f.

Using mathematical induction, prove that f(n)(x)=(x2+2nx+n(n−1))ex.
[7]
Using the result of (b), find the coordinates of any local maxima or minima on the graph of y=f(x).
[6]
Solve the equation f′′(x)=0.
[3]
Hence sketch the graph of y=f(x), indicating clearly the points found in (c).
[5]

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[Maximum mark: 24]

Consider the function f(x)=exx2, x∈R.

Let f(n) denote the nth derivative of f.

Using mathematical induction, prove that f(n)(x)=(x2+2nx+n(n−1))ex.
[7]
Using the result of (b), find the coordinates of any local maxima or minima on the graph of y=f(x).
[6]
Solve the equation f′′(x)=0.
[3]
Hence sketch the graph of y=f(x), indicating clearly the points found in (c).
[5]

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

I'm Plex, here to help with problems on this worksheet!