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Find an equation of the curve whose tangent line has a slope of f'(x) =2x^-10/11, given that the point ​(-​1,-4​) is on the curve.

3 answers

Your function is not written correctly, since (-1,-4) does not satisfy the equation. Try again.

In any case, f(x) is the antiderivative, and you can use the point to determine C.
maybe f'(x) = (2 x^-10)/11 ?
y = [(2/-9) x^-9 ]/11 + c
-4/2 = [1/ (-1)^9 ] /99 - c/2
-2 = -1/99 - c/2
c/2 = 1/99
c = 2/99
y = [(2/-9) x^-9 ]/11 + 2/99
y = -2 /99 x^-9 + 2/99
99 y = -2x^-9 + 2
duh. what was I thinking? SMH
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