Using graph of derivative, find where function is 0

[1MileCrash]

Homework Statement

[PLAIN]http://img850.imageshack.us/img850/2826/derivativegraph.png

Homework Equations

The Attempt at a Solution

I have 0 and 7, which it accepted as the lowest and highest values for x. I have no idea how to find the other.

 

[kru_]

Well, take a note of the values of f(x) for each integer. Notice where the function goes from positive to negative. Then, remembering that the derivative is the slope of the function, take a look at the value of the derivative at the points where f(x) switches from positive to negative. Some simple algebra should give you the point where it crosses the axis.

 

[Andrew Mason]

I don't see how you can answer this question unless you are given the value of f(0). Are you told that it is 0? All this graph tells you about f(0) is that the slope of f at x=0 is 1.

$$\int_0^x f'(x)dx = f(x) - f(0)$$

so:

$$f(x) = \int_0^x f'(x)dx + f(0)$$

The integral can be determined easily enough . You just need to be given f(0) to find f(x).

AM

 

[kru_]

I think it is given that f(0) = 0. At least, the poster said that the homework software indicated that 0 is a correct answer for the question which asks for a list of all zeros.

The way I read this, because the derivatives are all constant values between the integers, I can see that the slope of the function between the integers is a bunch of nice straight lines.

Then, since we know f(3) = 1 (by the answer to question 1), we can see that f(4) = 3, f(5) = 1 and f(6) = -1. That indicates that the function crossed the axis between x = 5 and x = 6. Since the slopes are constant between the integers, it means the function is made of nice straight lines, which should make the calculation of the exact crossing easy to find.

 

[1MileCrash]

So, somewhere between 5 and 6.

 

[kru_]

We know the value of the function at x=5. We know the value of the function at x=6. We also know the derivative of the function between 5 and 6 is a constant value, which indicates the function is a straight line between 5 and 6. From the graph we also know that the value of the slope is m = -2 between x=5 and x=6..

We can then use the point-slope form to determine the equation of the line from f(5) to f(6).

y - 1 = -2(x - 5)

solve for y

Then set y = 0 and solve for x..