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Ldaniel
for what value(s) of k will f(x)=x^3-kx^2+kx+k have an inflection point at x=5?
f(x)=x^3-kx^2+kx+k f ' (x)=3x^2-2kx+k ... derive f '' (x)=6x-2k ... derive again You want the point of inflection to be at x = 5, so you want f '' (5) = 0 f '' (x)=6x-2k f '' (5)=6*5-2k f '' (5)=30-2k 0=30-2k now solve for k