I am just starting Calculus in college and I have already run into a problem. I understand limits, but I don't understand anything about finding tangent lines and secant lines. I've tried to find help online, but I haven't found anything yet. It's an online class so the professor isn't very active. It's not like I can just ask him. If anyone could help me out, I'd GREATLY appreciate it. I have my first turn-in assignment due this week and I have no idea how to do it.
Tangents and Secants ... Please Help
- Thread starter Lizzie
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I appologize for being vague, but there isn't one specific problem, I don't understand tangents and secants at all...I guess if you need a problem to help me, then I'll give you number one on the turn in assignment.
1. The manager of a furniture factory finds that it costs $1200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph.
b)What is the slope of the graph and what does it represent?
c) What is the y-intercept of the graph and what does it represent.
*Feels so stupid*
1. The manager of a furniture factory finds that it costs $1200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph.
b)What is the slope of the graph and what does it represent?
c) What is the y-intercept of the graph and what does it represent.
*Feels so stupid*
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This question has nothing to do with tangents, secants, limits, or any other aspect of calculus. This is just algebra.
a) They've given you two points: (number, cost) = (100, 1200) and (300, 4800). Find the slope between the points, find the "y = mx + b" equation of the straight line through the points, and graph.
b) Read the slope "m" from the equation "y = mx + b" that you've just found. Recall what "slope" means. For every increase in x of one unit, what happens to y?
c) Read the y-intercept "b" off the equation "y = mx + b". Recall the value of x at the y-intercept. Review what "x" stands for in this particular case. Relate that value to what y stands for in this case.
Eliz.
a) They've given you two points: (number, cost) = (100, 1200) and (300, 4800). Find the slope between the points, find the "y = mx + b" equation of the straight line through the points, and graph.
b) Read the slope "m" from the equation "y = mx + b" that you've just found. Recall what "slope" means. For every increase in x of one unit, what happens to y?
c) Read the y-intercept "b" off the equation "y = mx + b". Recall the value of x at the y-intercept. Review what "x" stands for in this particular case. Relate that value to what y stands for in this case.
Eliz.
Oops, sorry.
Sorry about that.
2) Consider the function: y+f(x)=3x^2
a) What is the slope of the secant line connecting the points (1,3) and (2,12)?
So far I did this - (12-3)/(2-1) which gives me a slope of 9. Is that the slope of the secant?
b) What is the slope of the tangent line at the point (2,12)?
c) What is the equation of the tangent line at the point (2,12)?
Sorry about that.
2) Consider the function: y+f(x)=3x^2
a) What is the slope of the secant line connecting the points (1,3) and (2,12)?
So far I did this - (12-3)/(2-1) which gives me a slope of 9. Is that the slope of the secant?
b) What is the slope of the tangent line at the point (2,12)?
c) What is the equation of the tangent line at the point (2,12)?
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Do you mean "y = f(x) = 3x<sup>2</sup>"?
a) Yes, the slope of the line (secant or otherwise) through the two points is given by the slope formula.
b) The slope of the tangent line is the value of the derivative. So differentiate, and evaluate at x = 2.
c) Use the slope dy/dx = m from (b), along with the given point, to find the straight-line equation.
Eliz.
a) Yes, the slope of the line (secant or otherwise) through the two points is given by the slope formula.
b) The slope of the tangent line is the value of the derivative. So differentiate, and evaluate at x = 2.
c) Use the slope dy/dx = m from (b), along with the given point, to find the straight-line equation.
Eliz.
Answers
Ok, here's what I got for the first two problems.
1-a) y=18x-600
b) The slope of the graph is 18 and it represents the growth in price as the amount of chairs produced per day increases.
c) The y-intercept of the graph is -600 and it shows how many chairs per day are produced for zero dollars.
2-a) 9
b) ok, for this part, I took the derivative of 3x^2 (i don't know how to put the squared part up) and got 6x. Then, do I put in 2 for x to get 18 as the slope??
c) and I actually don't understand this part
Ok, here's what I got for the first two problems.
1-a) y=18x-600
b) The slope of the graph is 18 and it represents the growth in price as the amount of chairs produced per day increases.
c) The y-intercept of the graph is -600 and it shows how many chairs per day are produced for zero dollars.
2-a) 9
b) ok, for this part, I took the derivative of 3x^2 (i don't know how to put the squared part up) and got 6x. Then, do I put in 2 for x to get 18 as the slope??
c) and I actually don't understand this part
G'day, lizzie!
1(a)&(b) look good. The interpretation of the y-intercept in (c) can be difficult because it is negative. It almost says the company has a gain (negative cost) of $600 for not making any chairs and this continues to the x-intercept (of 33.33..). I recommend you sketch a graph of the situation. You will see with number of chairs on the x-axis and cost on the y-axis (from the calculations we have done), the y-intercept is actually showing you the cost when no chairs are produced. The x-intercept shows the number of chairs with zero dollars spent.
2(a)&(b) are good.
2(c). The straight-line equation is always useful:
y - y1 = m(x- x1)
Here you have a gradient of 18 (well done on that) and we're through the point (2,12). So substituting (x1,y1) = (2,12):
y - 12 = 18 (x - 2)
Rearrange to get it in them form y = mx + c.
Good luck!
1(a)&(b) look good. The interpretation of the y-intercept in (c) can be difficult because it is negative. It almost says the company has a gain (negative cost) of $600 for not making any chairs and this continues to the x-intercept (of 33.33..). I recommend you sketch a graph of the situation. You will see with number of chairs on the x-axis and cost on the y-axis (from the calculations we have done), the y-intercept is actually showing you the cost when no chairs are produced. The x-intercept shows the number of chairs with zero dollars spent.
2(a)&(b) are good.
2(c). The straight-line equation is always useful:
y - y1 = m(x- x1)
Here you have a gradient of 18 (well done on that) and we're through the point (2,12). So substituting (x1,y1) = (2,12):
y - 12 = 18 (x - 2)
Rearrange to get it in them form y = mx + c.
Good luck!
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Yes, "x -> 3<sup>+</sup>" means "as x approached three from the right". A superscripted "minus" sign would indicate "from the left".
For which problem is there an asymptote at x = 2? I cannot locate this in the thread to this point. Please clarify. It would probably help if you posted the entire question, including the instructions, all in one post. Thank you.
Eliz.
For which problem is there an asymptote at x = 2? I cannot locate this in the thread to this point. Please clarify. It would probably help if you posted the entire question, including the instructions, all in one post. Thank you.
Eliz.