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Question Number 196464 by mokys last updated on 25/Aug/23
if f(x)= x^3 +x^2 , g(x)= f^(−1) (x) , find g^′ (3) ?
iff(x)=x3+x2,g(x)=f−1(x),findg′(3)?
Answered by Frix last updated on 25/Aug/23
y=x^3 +x^2 dy=x(3x+2)dx g′(x)=(dx/dy)=(1/(x(3x+2))) x^3 +x^2 =3 ⇒ x=−(1/3)+((((79)/(54))+((√(77))/6)))^(1/3) +((((79)/(54))−((√(77))/6)))^(1/3) x≈1.17455941 g′(x)≈.154133358 [This is the real solution of r^3 +(r/(231))−(1/(231))=0]
y=x3+x2dy=x(3x+2)dxg′(x)=dxdy=1x(3x+2)x3+x2=3⇒x=−13+7954+7763+7954−7763x≈1.17455941g′(x)≈.154133358[Thisistherealsolutionofr3+r231−1231=0]

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