I need calculus help, please!?

Question

I have to fix an essay I wrote and I'm having difficulty finding the information. Here are the specific questions I need to complete:
-Define what a tangent line is
-Explain why the derivative is the instantaneous rate of change and the secant is the average rate of change.
-Explain why velocity is the first derivative of displacement and why acceration is the second.
-Why does the derivative being zero yield a minimum or maximum?
-Finally, what is calculated by the definite integra if the function is negative for every value between points a and b?

I am a true math-phobe so this is not fun for me! Any help would be greatly appreciated! I have visited tons of websites, but they all have this assumption that the viewer has some basic understanding of calc- I have NONE!

Thanks!
CC

This class is part of my Science Endorsement I am working towards. If I had a choice, I would not be taking it!

Answer 1

Try Michael Kelley's website at this link: http://www.calculus-help.com/funstuff/phobe.html. He also has a very easy to read book on calculus called "The Complete Idiot's Guide to Calculus". He's one of the few guys who didn't forget how to speak English as soon as they learned how to speak in "Math".

Lesson 1 under Finding Derivatives illustrates the difference between a secant line and a tangent line, and the lesson explains what we're trying to find with derivatives.

Answer 2

If you are a math phobe, why are you taking calculus?

A tangent line is a line that touches a curve and at the point where it touches the curve shares the same instantaneous slope.

The derivative is an instantaneous rate of change in that it measures the slope of a function at a specific point. The secant is the average rate of change because it takes the slope between two points of a function and therefore averages the slope of the function.

The rate of change per time in space is defined as the velocity of an object, Therefore the derivative of space with respect to time is velocity. The rate of change per time of velocity is acceleration. Therefore the derivative of velocity with respect to time is acceleration.

When a derivative is zero, a function has a slope of zero. That usually means that at that point the function is changing from increasing to decreasing or vice versa. However, it could also mean the the function is increasing, levels off, then increases again, or the same with decreasing, or that the function is a straight line with a slope of O.

The area between the function , the line x=a, the line x=b and the line y=0 is calculated.

Answer 3

well well
-a tangent line is a line which when drawn to circle it touches it only at one point. i have taken a circle as an example because it can give you a good picture of what i am talking about, but it can be drawn to a parabolic graph or hyperbolic graph. the only thing u have to know is that it touches the graph at one point and never crosses it. I hope we are together.
-velocity is the first derivative of a displacement because, when we find the derivative of this displacement we differentiate it with respect to time that is to say change of distance per unit time (dx/dt)
-the second derivative of displacement is the first derivative of velocity which means now we look at the rate of change of velocity(aka acceleration).let me explain more about this when you want to get the second derivative of a function you must defferentiate the function two times, the first time u diff is when u get the velocity and the second time u get acceletation.

-Why does the derivative being zero yield a minimum or maximum? first you must know what does maximum or minimum mean. these are points where the graph changes direction (if it was going down it starts going up and vice versa). so if you get the derivative equal to zero this means at that point there is no slope in other words whaen you draw a tangent line at this point it will be parallel to the x-axis. to know if that point is a maximum or minimum just change the values of x, if it was 4 then try 3.5 and 4.5 if both of them gives you a negative number then that is a maximum point.

Answer 4

A tangent is a straight line that intersects a curve at exactly one point. [for your purposes]

The derivative is the rate of change in "delta y" as the "delta x" approaches zero (by definition). This is the rate of change at exactly one point, or "instantaneously" if x represents time.

The secant is the rate of change in "delta y" as "delta x" is a given range. Thus, it's the average change in y over the interval in x.

If something is changing position, you want to know what its change is per time. This is the secant. If you want to know its rate in change at a given moment, this is the derivative.
If something's velocity is changing (it's accelerating), you need the derivative of the velocity [which is the 2nd derivative of displacement].

Derivative = 0 means that the curve's tangent =0 at a point. It doesn't always mean a min or max. It could be a change in curvature of the curve (like y=x^3). However, at a min or max, the curve will always have a 0 derivative. In a quadratic equation, it means that the y increment is changing between positive and negative. That means you must be at a point of greatest value or least value.

I don't know the answer to the last question.

Answer 5

A tangent line is a line that touches a curve at single point
The derivative is df(x)/dx is change in function f(x) at any point on the curve f(x), You can get value at point x=x1 by putting x=x1. whereas secant is between two points, it could be between x=x1 and x=x2.
rate of change of displacement w.r.t. time ds/dt is velocity and rate of change of velocity w.r.t. time dv/dt or d2s/dt2 is acceleration.
Zero derivative means chane of function at that point is zero, i.e. slop of curve is zero, means either it is max or min.
it is area between curve f(x) and x-axis, between lines x=a and x=b

Answer 6

Tangent Line:
A line going through a point on a cure that tells what the slope of the curve is.
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Secant Line:
Is a line draw through 2 points on a curve, the line segment under the curve. It is used to approximate the Tangent line.
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Derivative:
Gives the slope of the tangent.

Anyway, try http://en.wikipedia.org they are good at explaining it.

Answer 7

refer to this book
Introduction to Calculus and Analysis by Courant and John