Posted by patel on Saturday, September 22, 2012 at 11:57pm.
f(1) = -2
f(2) = 134
so there is indeed at least one root in [1,2]
f'(x) = 7x^6 + 7
f'(x) > 0 everywhere, so f(x) is strictly increasing.
Since f(2) is so much greater than f(1), I'd expect to find the root near 1
f(1) = -2
f(1.05) = -1.243
f(1.10) = -0.352
f(1.15) = +0.710
so, there is a root in [1.05,1.15]
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