Question

how to find f(x) values of a graph of f'(x)

Answer 1

Calculate the area under the graph.

Answer 2

so calculate the area under the line

Answer 3

\[\int_a^b f'(x)\ dx = f(b) - f(a)\]

Answer 4

Yes you are calculating the area under the line/curve.

Answer 5

so if f"(x) =2 then the area under that is 2?

Answer 6

The concept of area only makes sense for an interval of the function.

Answer 7

If you take the antiderivative of the function, then you can find the f(x) values.
Let me explain.

For instance, f'(x) = 2x
We know that the derivative of x^2 is 2x by the power rule.
Then we can just use the power rule backwards to do a simple antiderivative.

2x^1+1/1+1 = x^2 which is our original equation f(x).

You take the power of the variable, raise it by one, and then divide by the new power of the variable.

There are other ways which are easier to do this, but I am assuming that you are in differential calculus.

Hope this helps.
http://www.tutorsean.net

Answer 8

He was asking how you would find the values via a graph, not how to evaluate an integral.

Answer 9

yeah i only have a graph to work from

Answer 10

You can look for the intervals of concavity and for critical points, that is x-intercepts, and use that to find the behavior of the original function. This is how we did it in my calculus class a couple years back.