Hey guys, I was wondering if you could help me figure out a few math problems. I am currently in InteractiveMathematicsProgram 3 (11th grade) and I'm having trouble with tangents and secant lines; here is a transcript of my homework (my thoughts in bold):
A secant for the graph of a function is the line (or line segment) connecting two points on the graph. A tangent is a line that "just touches" the graph at a point. This assignment explores the two concepts and their connections with derivatives.
I already knew this, and understand the concept of what both of these are, as they were shown to me in class.
Here is the assignment:
1. Consider the function f defined by the equation f(x) = 0.5x^2.
This seems easy enough to understand, my issues start below.
A.
Sketch the graph of this function, with the scale on your x-axis going from -1 to 3. Use a full size sheet of graph paper for this sketch so that you will be able to get enough detail in Question 1c.
So I have a graph in front of me, where the x axis is going from -1 to 3, what should the y axis be? I assume 2, due to the next question.
B. Label the point (2,2) on your sketch.
Easy enough, nothing too tough yet.
C. The points listed here are also on the graph. In each case, draw the secant line connecting the given point to (2,2) and find the slope of that secant.
i. (0,0)
ii. (1,0.5)
iii. (1.5, 1.125)
iv. (1.9, 1.805)
Now what do I do here? I forgot how to find slope, and I don't really know what this is supposed to look like when drawn. Can anyone draw a picture for me to help me out? Thanks.
D. Draw the line that is tangent to the graph at (2,2). Then estimate the slope of that line and explain your reasoning.
I just plain don't know how to do this, can someone help me out?
E. Find the derivative of the function f at the point (2,2).
How do I do this, too?
Sorry for so many questions, but I have a final coming up this thursday, and not only does this HW assignment make the difference between a B and a C on my report card, but it also reminded me of how much I need to remember before the final so I don't fail. Thanks a lot, everyone! I hope to be trying to help you soon (even with my limited math knowledge )
A secant for the graph of a function is the line (or line segment) connecting two points on the graph. A tangent is a line that "just touches" the graph at a point. This assignment explores the two concepts and their connections with derivatives.
I already knew this, and understand the concept of what both of these are, as they were shown to me in class.
Here is the assignment:
1. Consider the function f defined by the equation f(x) = 0.5x^2.
This seems easy enough to understand, my issues start below.
A.
Sketch the graph of this function, with the scale on your x-axis going from -1 to 3. Use a full size sheet of graph paper for this sketch so that you will be able to get enough detail in Question 1c.
So I have a graph in front of me, where the x axis is going from -1 to 3, what should the y axis be? I assume 2, due to the next question.
B. Label the point (2,2) on your sketch.
Easy enough, nothing too tough yet.
C. The points listed here are also on the graph. In each case, draw the secant line connecting the given point to (2,2) and find the slope of that secant.
i. (0,0)
ii. (1,0.5)
iii. (1.5, 1.125)
iv. (1.9, 1.805)
Now what do I do here? I forgot how to find slope, and I don't really know what this is supposed to look like when drawn. Can anyone draw a picture for me to help me out? Thanks.
D. Draw the line that is tangent to the graph at (2,2). Then estimate the slope of that line and explain your reasoning.
I just plain don't know how to do this, can someone help me out?
E. Find the derivative of the function f at the point (2,2).
How do I do this, too?
Sorry for so many questions, but I have a final coming up this thursday, and not only does this HW assignment make the difference between a B and a C on my report card, but it also reminded me of how much I need to remember before the final so I don't fail. Thanks a lot, everyone! I hope to be trying to help you soon (even with my limited math knowledge
)