Question

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

Answer 1

What's the slope of the given line?

Answer 2

m=-1

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

oh..i get it...

Answer 7

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

Answer 8

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

Answer 9

That will do!! Good work.

Answer 10

thank you for helping me^^

Answer 11

:-)