graphing integrals and derivatives (1 Viewer)

[oredbayz]

hey BOS,

does anyone have a set of rules for graphing the integral or derivative of original function f(x) without knowing the formula, with just the graph given

thanks in advance

 

[icycledough]

For graphing the derivative of an original function, there's a few tips I can give you:

• When there's a peak (concave up or down), the derivative will be 0 (a horizontal line), so you can mark this as a point on the x axis, directly above or below the peak
• I would then draw a dotted line from the peaks of the original function vertically down, so you can see the derivative of the parts of the original function on either side of the peaks

I came across a website which explains it quite well: https://www.expii.com/t/sketching-the-derivative-of-a-function-141

Graphing the integral of a function adds a layer of difficulty, so I'll let someone else put in their advice.

 

[stupid_girl]

Graphing the integral (anti-derivative) doesn't add much difficulty.

Suppose you are given f'(x) and you need to graph f(x).
When f'(x) is positive, f(x) is increasing (and vice versa).
When f'(x) is increasing, f(x) is concave up (and vice versa).

 

[5uckerberg]

I will add another point if f'(x)=0 then we will need to apply where is the value to the right of and where is the value to the left of . This is done so we can determine whether a point is the minimum turning point and the maximum turning point.

is the point where f'(x)=0