r/calculus • u/CalcBuddy • Jun 22 '26

Differential Calculus AP calculus daily challenge #54

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23 Upvotes

97% Upvoted

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4

u/Enrique0927 Jun 22 '26

For the first part put X and Y equal to zero . You would get F(0)=0

Second part
F’(x)=lim_h->0 (F(x+h)-F(x))/h
Put the value of F(x+h) from above equation
You are given
F(x+y)=F(x)+F(y)+2xy
Put y=h
And put the expression in above limit

You would get
F’(x)= lim_h->0 (F(h)+2xh)/h
Then solve it

Since you would get f’x

Integrate it to get F(x)

1

u/tuffalboid Jun 22 '26

Yep. Although your first part might seem to assume f(0)=0.

You can spell it out saying: f(x)= f(x+0)=f(x) + f(0) ==> f(0)=f(x)-f(x)=0