SOLUTION: Please help me solve this problem: Graph three members of the family of curves that have f(x)= -x + 1 as a common derivative.

Algebra ->  Test -> SOLUTION: Please help me solve this problem: Graph three members of the family of curves that have f(x)= -x + 1 as a common derivative.       Log On


   

Question 1005853: Please help me solve this problem:
Graph three members of the family of curves that have f(x)= -x + 1 as a common derivative.
Found 2 solutions by ikleyn, AnlytcPhil:
Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
.
Graph three members of the family of curves that have f(x)= -x + 1 as a common derivative.
----------------------------------------------------------------

The plots below show three such functions:

f%5B1%5D%28x%29 = -%281%2F2%29x%5E2+%2B+x,   f%5B2%5D%28x%29 = -%281%2F2%29x%5E2+%2B+x+%2B+1   and   f%5B2%5D%28x%29 = -%281%2F2%29x%5E2+%2B+x+%2B+2.

They differ in a constant term.




Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)= -x + 1 

"-x + 1" is the sum of -x and 1.

If we take the derivative of x² we get 2x.
But we want -x, not 2x, So we must take the
derivative of expr%28-1%2F2%29x%5E2 to get -x.

So we need the term expr%28-1%2F2%29x%5E2.

To get the 1 we must take the derivative of x.

So the function expr%28-1%2F2%29x%5E2%2Bx would be such
a function.

However since the derivative of a constant is zero,
we could have any constant added to that.  So here
are some answers:

expr%28-1%2F2%29x%5E2%2Bx%2B1
expr%28-1%2F2%29x%5E2%2Bx-7
expr%28-1%2F2%29x%5E2%2Bx%2B35
expr%28-1%2F2%29x%5E2%2Bx-12
expr%28-1%2F2%29x%5E2%2Bx%2B1000

Edwin