how to find a function f such that f'(x)=x and the line y+x=2 is tangent to the graph of f??

Question

tkhunny · Answer

What's the slope of the given line?

syaza97 · Answer

m=-1

tkhunny · Answer

What value of x makes f'(x) = -1?

syaza97 · Answer

oh...i thought you ask for the slope of tangent...the question did not give any slope value...

tkhunny · Answer

You were doing just fine.
What is the slope of the given line, m = -1 -- Perfect.
What value for x gives f'(value) = -1?  x = -1
What point on the line has x = -1?  y = 3.

There is your task.  Find a function that has f'(-1) = -1 and f(-1) = 3

You might try the antiderivative.

syaza97 · Answer

oh..i get it...

tkhunny · Answer

Let's see it...  You can do it!

syaza97 · Answer

i got $$f(x)=\frac{ x ^{2} }{ 2 }+\frac{ 5 }{ 2 }$$

tkhunny · Answer

That will do!!  Good work.

syaza97 · Answer

thank you for helping me^^

tkhunny · Answer

:-)