Find the derivative of the inverse of the given function at the given point? f(x)=5x+3x^23x2+7x+2 at (13,1) help me please

1 Answer
Dec 25, 2017

1/(2sqrt 69)1269

Explanation:

Write f(x)=y= 3x^2 +12x+2= 3(x^2 +4x)+2=3(x^2 +4x +4) -10=3(x+2)^2 -10f(x)=y=3x2+12x+2=3(x2+4x)+2=3(x2+4x+4)10=3(x+2)210

Thus, the given function is y=3(x+2)^2 -10y=3(x+2)210. For finding inverse of f(x), interchange 'x' and 'y' ad the solve for 'y'. Accordingly, it would be x=3(y+2)^2 -10x=3(y+2)210. Therefore f^-1(x)f1(x)=y=sqrt((x+10)/3) -2y=x+1032. This represents an horizontal parabola with its vertex at (-10,-2).

derivative would be y'=1/sqrt 3 1/2 (x+10)^(-1/2)

At the given point (13,1) y'=1/sqrt 3 1/2 1/sqrt 23=1/(2sqrt 69)