Posted by **Stuck** on Saturday, April 3, 2010 at 9:06pm.

"The line x+y = 0 is tangent to the graph of y = F(x). Find F(x) if F'(x) = x".

I know how to find the antiderivative of F'(x), but I don't know how to use the tangent line to find my constant.

- Calculus -
**bobpursley**, Saturday, April 3, 2010 at 9:11pm
so the line x+y gives a slope of -1

f(x)=1/2 x^2+c but at some x, the tangent line has a slope of -1

f'= x so x=-1

what is y when x=-1? y=1

so the point of tangency is -1,1

f(x)=1/2 x^2 + C

1=1/2+C

C= 1/2

check my thinking.

- Calculus -
**Stuck**, Saturday, April 3, 2010 at 9:24pm
Thank you! That makes sense!

## Answer This Question

## Related Questions

- Calculus AB - Sorry but I've got a lot of problems that I don't understand. 1) ...
- Calculus - The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), ...
- Calculus - 55. Find an equation of the tangent line to the graph of f(x) =x^3 - ...
- Math- calculus - Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an...
- Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...
- Calculus - Let f(x)=3x^4-2x^2+3 a) find f'(x) Answer: f'(x)=12x^3-4x b) find the...
- calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...
- Calculus - Given the function y=(x^2-5/x+3), answer the following questions. a) ...
- calculus - 1. Which of the following expressions is the definition of the ...
- cal - find the equation of a quadratic function whose graph is tangent at x=1 to...

More Related Questions