Find the function with the given derivative whose graph passes through the point p g'(x)= 1/x^21x2+2x ,p(-1,1) HELP ME PLEASE??

3 Answers
Dec 9, 2017

g(x) = -x^-1+x^2-1g(x)=x1+x21

Explanation:

We have

int g'(x)dx = g(x) = int (x^-2+2x)dx = -x^-1+x^2+C_0 but

g(-1) = 1 rArr -(-1)^-1+(-1)^2+C_0 = 1 and then

C_0 = -1 so the sought function is

g(x) = -x^-1+x^2-1

Dec 9, 2017

See below.

Explanation:

If g'(x)=1/x^2+2x, then g(x)=int(1/x^2+2x) dx

int(x^(-2)+2x)dx=-x^(-1)+x^2+c=-1/(x)+x^2+c

g(x)=-1/x+x^2+c

If g(x) passes through point P (-1,1) then:

1=-1/(-1)+(-1)^2+c

1=1+1+c=>c=-1

g(x)=-1/x+x^2-1

Dec 9, 2017

g(x)=x^2-1/x-1

Explanation:

I'll do it without integral usage (in case you need it that way)

Graph C_g passes trough P(-1,1) so that means g(-1)=1

We have g'(x)=1/x^2+2x ,

(g(x))' = (-1/x)' +2*(x^2/2)'

(g(x))'=(x^2-1/x)'
g,x^2-1/x continuous and differentiable
and (g(x))'=(x^2-1/x)' so there is one c inRR for which

g(x)=x^2-1/x+c

  • g(-1)=1 <=> c+2=1 <=> c=-1

Eventually g(x)=x^2-1/x-1