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

[xtrmk]

Given a graph of f', the derivative of f, how do I find the f value such as f(-3) and f(4) with its derivative graph? Is it the slope?

also, how would I find the equation for the line tangent to the graph of f at a certain point? Any help is appreciated. thanks

 

[stapel]

Without seeing the graph and any other information you might have, it's difficult to answer. In general, however, one cannot find the value of the function from only the derivative. That's kind of the point of the constant "C" of integration.

Eliz.

 

[xtrmk]

[/url][/img]

This is the graph. Any help is appreciated with my questions

 

[stapel]

Unfortunately, since we have no data points regarding the actual function, there is no way to guess what the integration (anti-differentiation) constant might be.

For instance, f(x) = x² + 3 and g(x) = x² - 4 both have the derivative h(x) = 2x. But would there be any way to tell, from only the graph of the derivative, which function you'd started with? No.

Same deal here. Without other information, there is no way to answer your question. Sorry.

Eliz.

 

[xtrmk]

Without other information, there is no way to answer your question. Sorry.

Sorry the only data point of f given is f(0) = 3.

Could you help me proceed? Thanks

 

[stapel]

...the only data point of f given is f(0) = 3.

Ah; so there was more information.... It really does help to provide the whole question.... :?

Since the derivative of the left-hand half appears to be a straight line, what then would probably be safe to assume about the original function?

Since the derivative of the right-hand half appears to be the top half of a circle or (more conveniently) the top of a parabola, what then would probably be safe to assume about the original function?

Unfortunately, we cannot tell to which half the given data point belongs. But assuming the function is continuous, what can you figure out about the constants of integration for either half of the function?

What then do you get for the values at the requested points?

Eliz.

 

[xtrmk]

...the only data point of f given is f(0) = 3.

Ah; so there was more information.... It really does help to provide the whole question.... :?

Since the derivative of the left-hand half appears to be a straight line, what then would probably be safe to assume about the original function?

Since the derivative of the right-hand half appears to be the top half of a circle or (more conveniently) the top of a parabola, what then would probably be safe to assume about the original function?

Unfortunately, we cannot tell to which half the given data point belongs. But assuming the function is continuous, what can you figure out about the constants of integration for either half of the function?

What then do you get for the values at the requested points?

Eliz.

Left something with -x slope?
Right something with -x^2 ?
Would the constant be 3 ?
Still confused on how to get the f(-3) and f(4) value and a line tangent to graph of f at point (0,3)