Question

Given that x+y= 0 is tangent to y=F(x), find F(x) if F'(x) = x

Answer 1

how do u find the antiderivative of y?

Answer 2

Have you taken up the Fundamental Theorem of Calculus?

Answer 3

integrate to find F(x)

\[\int\limits x dx\]

use the tangent properties to evaluate the constant

Answer 4

yes i have

Answer 5

\[F(x) = \frac{1}{2}x^{2} +\frac{1}{2}\]

Answer 6

how did you get this answer? Can someone explain step by step?

Answer 7

\[F(x) = \int\limits_{}^{}x = \frac{1}{2}x^{2} +C\]
F'(x) = slope of tangent line = -1
--> x = -1
x+y =0
-1 + y = 0
y = 1

so plug in the point and solve for C
1 = 1/2*(-1)^2 +C