Posted by **maggie** on Friday, February 4, 2011 at 12:38am.

On the graph of f(x)=3sin(2x), points P and Q are at consecutive lowest and highest points with P occuring before Q. Find the slope of the line which passes through P and Q.

- calculus - slope -
**MathMate**, Friday, February 4, 2011 at 6:23am
We will start with the general case of the function sin(x).

The minima (lowest points) of the graph of sin(x) occurs at

x=xmin=3π/2+2kπ where k∈ℤ (i.e. k=integer)

The maxima (highest points) of sin(x) occurs at

x=xmax=π/2+2kπ where k∈ℤ.

Two consecutive minimum/maximum could therefore occur at xmin=3π/2 and xmax=5π/2.

The given function is 3sin(2x), so

2x=3π/2, or x1= 3π/4 for minimum.

The ordinate at this point is

f(x1)=3sin(2*3π/4)=-3

Therefore x1(3π/4,-3).

and

2x=5π/2, or x2= 5π/4 for maximum.

The ordinate at this point is

f(x2)=3sin(2*5π/2)=3

Therefore x2(5π/4,3)

The slope is therefore

m=(y2-y1)/(x2-x1)

=(3-(-3))/(5π/4-3π4)

=3.82

Check my calculations.

## Answer this Question

## Related Questions

- calculus - On the graph of f(x)=7sin(7pi x), points P and Q are at consecutive ...
- calculus - On the graph of f(x)=6sin(8πx), points P and Q are at ...
- Calculus 1 - On the graph of f(x) = 8*sin(3pi*x), points P and Q are at ...
- math - i have more than one question so if u no any of the answers please tell ...
- Algebra - 1. Is it more difficult to run up a ramp with a slope of 1/5 or a ...
- math - 1. What is the slope of the line that passes through the points (-2, 5) ...
- Math 101 - Find the equation for each of the following items below: a. A line ...
- Algebra - A line passes through the points (-10, -4) and (-1, 2). What is the ...
- algebra - what is the slope of a line that passes through the points (-4,-3), (4...
- Algebra.. - Find the slope of the straight line that passes through the given ...

More Related Questions