Tangent lines, Mathematics

Recall also which value of the derivative at a specific value of t provides the slope of the tangent line to the graph of the function at that time, t. Thus, if for some time t the velocity occurs to be 30 m/s the slope of the tangent line to the graph of the velocity is 3.92.

We could carry on in this fashion and pick various values of v and calculate the slope of the tangent line for such values of the velocity. Although, let's take a slightly additionally organized approach to that. Let's first identify the values of the velocity which will have zero slope or horizontal tangent lines. These are easy adequate to determine. All we require to do is set the derivative equivalent to zero and resolve for v.

In the case of our illustration we will have only one value of the velocity that will have horizontal tangent lines, v = 50 m/s. What it means is that IF (again, there's that word if), for several time t, the velocity occurs to be 50 m/s after that the tangent line at that point will be horizontal. What the slope of the tangent line is at times before and after this point is not identified yet and has no bearing on the slope at this exact time, t.

Thus, if we have v = 50, we identify that the tangent lines will be horizontal. We indicate this on an axis system along with horizontal arrows pointing toward increasing t at the level of v = 50 as demonstrated in the subsequent figure.

182_tangent lines.png

Here, let's find some tangent lines and thus arrows for our graph for some another value of v. At that point the only precise slope that is helpful to us is where the slope horizontal. Consequently instead of going after exact slopes for the rest of the graph we are only aimed at go after general trends in the slope. Is the slope decreasing or increasing? How quick is the slope decreasing or increasing? For this illustration those kinds of trends are extremely easy to find.

Posted Date: 4/10/2013 3:14:54 AM | Location : United States

Related Discussions:- Tangent lines, Assignment Help, Ask Question on Tangent lines, Get Answer, Expert's Help, Tangent lines Discussions

Write discussion on Tangent lines
Your posts are moderated
Related Questions
What is the least number of students needed in a class to be sure that at least 6 will receive similar grade if there are five probable grades A, B,C, D and F?  Ans: Let us re

a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle

Example of Word problem: There is a man who is 21 years older than his son.  5 years ago he was four times as old as his son. How older are both now? Solution: Step 1

Determine the value of the unknown side of a right triangle: The two legs of a right triangle are 5 ft and 12 ft.  How long is the hypotenuse? Now Let the hypotenuse be c ft.

Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for

Average Function Value The first application of integrals which we'll see is the average value of a function. The given fact tells us how to calculate this. Average Functi

What is Plotting Points ? How would you go about drawing the graph of y = x2 ? One way to do it is by plotting points. (Your graphing calculator uses this method.) This is

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Graphical Method While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependen