When shown the graph of f(x), how can u sketch the graph of f'(x), if u aren't given the equation of f(x)?

Question

When shown the graph of f(x), how can u sketch the graph of f'(x), if u aren't given the equation of f(x)?

I know how to find the zeros, and where it is increasing and decreasing, but how can u find certain points?

Answer 1

The derivative is the slope of the function at a given point. So, hold your ruler tangent to the graph, find the slope of the ruler, and that gives you f' at that point. If it's hard for you to see whether the ruler is tangent to the line, try fixing one end of the ruler to the graph at the x-coordinate you're trying to measure, and then rotate the ruler until it just barely fails to cross the graph - that gives you the tangent line.

Answer 2

The graph of f'(x) is going to be 0 at the relative maximums and relative minimums. On each side of the point, determine whether the slope is positive or negative. Since you are really just graphing the slope, make your values positive or negative according to the slope at each value. Finally consider points of inflection..( where the graph goes from holding water to spilling water). These will be the relative minimums and/or relative maximums of your graph of f'(x). Now just fill in.
A suggestion; try to find an equation that has a graph that looks something like your graph. Take the first and second derivatives and then graph the first derivative.
If you don't know about second derivatives, I haven't helped you at all. Now your only hope is to try to determine the slope of the line at a bunch of points and to graph the values of these slopes. f'(x) can be though of as the slope of f(x) at each point on the graph. (Really the slopes of the tangents to each point.)
Good luck!

Answer 3

As far as I'm concerned, it is very possible to sketch the graph of f'(x) if you have f'(x).

f'(x) = the slope of the original f(x)

So wherever the graph is increasing and pointing up in a straight linear path, that is one constant y value.

For example if the graph has a maximum or a mininum, that is where the f'(x) graph would be a hoirzontal line at zero at the same domain where the max and min was in the original.

Answer 4

So the function is f(x) = 2^(x - a million) permit's attempt some values of x: a million) f(x) is defined for all factors: there are no holes or undefined values. 2) f(x) is often extra effective then 0, never 0 yet very on the factor of 0 3) while x is damaging f(x) turns into very small 0 -> a million/2 +a million - > a million +10 -> 2^9 (enormous selection) -10 -> a million/2^11 (small selection)

Answer 5

well...i start with finding all the intervals where the derivitive is 0 -- f(x) is a horizontal line.
then i look for places where the slope is constant...
it is hart to explain without seeing the graph of f(x)
let me try anyway
suppose you know that the derivitive over the interval [a,b] is 2x, then at a point c which is in the interval [a,b] the derivite at c is 2c.
i hope this helps -- sorry it is kind of vague