Graph of the Derivative (1 Viewer)

[nrlwinner]

Can somebody teach me some general tips in reading the graph of the derivative.

 

[ninetypercent]

do u mean stuff like stationary points on the graph are x intercepts on the graph of the derivative?

 

[adomad]

post a question

 

[nrlwinner]

do u mean stuff like stationary points on the graph are x intercepts on the graph of the derivative?

Yeah like that. What else do I have to know?

 

[x jiim]

Umm. When the graph of the derivative is positive, the graph of the function is going up and vice versa. And the closer the graph of the derivative is to 0, the less steep it is? Try as I might, I can't get that to sound intelligent. Oh well.

 

[nrlwinner]

Well here are some queries.

If the slope of the graph of f'(x) is negative, what about the slope of f(x)

What does the x-intercept of f'(x) indicate?

What does the stationary point of f'(x) indicate?

If the graph of f'(x) is above the x-axis, what does it indicate?

 

[x jiim]

Well here are some queries.

If the slope of the graph of f'(x) is negative, what about the slope of f(x)

The slope of f(x) is getting less steep/levelling out if f'(x) is positive, reaching a stationary point where f'(x) is 0. The function is still going up, but not by as much. Like, I don't know, a rollercoaster reaching the top of a hill or something.
The slope of f(x) is getting steeper if f'(x) is negative; the function is going down, faster I guess you'd call it?

What does the x-intercept of f'(x) indicate?

At f'(x) = 0, there is a stationary point on the graph of f(x) where it is parallel to the x-axis, not increasing or decreasing.

What does the stationary point of f'(x) indicate?

The gradient of the gradient is 0. I think there's something about drawing a tangent here? Well, it's like a straight part of the function, but not [usually] in a nice horrizontal/vertical direction.

If the graph of f'(x) is above the x-axis, what does it indicate?

The function f(x) is going up.

Gosh, that was confusing to type out =\

 

[Lukybear]

Well here are some queries.

If the slope of the graph of f'(x) is negative, what about the slope of f(x)

Graph is concaving down. f''(x)<0 = the slope of f'(x) <0

What does the x-intercept of f'(x) indicate?

Stationary Pts of f(x). When f'(x) = 0, there is a turning pt. If it is a decreasing from right to left, then there is a gradient at right and negative gradient at left.

What does the stationary point of f'(x) indicate?

A pt of inflexion. When f''(x) = 0 a pt of inflexion exist

If the graph of f'(x) is above the x-axis, what does it indicate?

Gradient above 0.

 

[nrlwinner]

Thanks for the info. In an unrelated question,

How do you find the lim as x approaches infinity, or the asymptote, of

x^2 - y^2 + xy = 5