1yeah.. plz explain!!!
Assume that p is a real number. In order for 3√x+3p+1 - 3√x=1 to have real solutions it is necessary that
1. p≥1/4
2. p≥-1/4
c. p≥1/3
4. p≥-1/3
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4 Answers
62\\f(x)=(x+a)^{1/3}-x^{1/3} \\f'(x)=1/3(x+a)^{-2/3}-1/3x^{-2/3}=0 \\(x+a)^{2/3}=x^{2/3}\Rightarrow(x+a)^2=x^2\Rightarrow x=-a/2
Once we have found the point of maxima, we try to find the value of the maxima...
this is given by 2(a/2)^{1/3} which is 1 in the current problem
hence a/2=(1/2)3 or a =1/4
Now in the current question, a=3p+1
So 1/4=3p+1 or p=-1/4
That is the minimum value of p
11Simply cubing gives us a quad in x1/3.....now plug in the fact that D≥0, to get b).