Posted by rimmel on Sunday, November 15, 2009 at 1:52pm.
I would estimate it using the first two terms of a McLaurin series expansion:
f(4.013) = f(4) + (4.013-4) f'(x)
= f(4) + 0.013 f'(4)
where f(4) = 2, and
f'(4) = 4f(4) + 2*4 = 16
So, f(4.013) = 2 + 0.013*16 = 2.208
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