Mathematics, 05.02.2020 21:48 qloc

Estimate the instantaneous rate of change of h (t) = 2t² + 2 at the point t = −1.
in other words, choose x-values that are getting closer and closer to −1 and compute the slope of the secant lines at each value. then, use the trend/pattern you see to estimate the slope of the tangent line.

Answers: 3

Show answers

Answers

Answer from: SumayahAminaAnsari

The instantaneous rate of change of h(t) = 2t² + 2 at the point t = −1 is -4.

Step-by-step explanation:

If two distinct points P(x_1,y_1) and Q(x_2,y_2) lie on the curve y=f(x) , the slope of the secant line connecting the two points is

$m_{sec}=\frac{y_2-y_1}{x_2-x_1}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

If we let the point x_2 approach x_1 , then Q will approach P along the graph f(x). The slope of the secant line through points P and Q will gradually approach the slope of the tangent line through P as

$m_{tan}= \lim_{x_2 \to x_1}\frac{f(x_2)-f(x_1)}{x_2-x_1}$

And this is the instantaneous rate of change of the function f(x) at the point x_1 .

From the information given, we know that the point P (-1,2(-1)^2+2)=(-1,4) lies on the curve h(t) = 2t^2 + 2 .

If Q is the point (t, 2t^2 + 2) we can find the slope of the secant line PQ for the following values of t. Because we choose values that are getting closer and closer to −1.

$\begin{array}{c}-0.9&-0.99&-0.999&-0.9999\\-1.1&-1.01&-1.001&-1.0001\\\end{array}\right$

Let the point P be (x_2=-1, y_2=4) and the point Q be (x_1=t, y_1=2t^2+2) . So,

$m=\frac{4-(2t^2+2)}{-1-t}\\\\m=-\frac{2\left(t+1\right)\left(t-1\right)}{-1-t}\\\\m=2\left(t-1\right)$

Next, substitute the value of x in the formula of the slope

m=2(-0.9-1)=-3.8

Do this for the other values of x.

Below, there is a table that shows the values of the slope.

From the table, as t approaches -1 from the left side (-0.9 to -0.9999), the slopes are approaching to -4 and as t approaches -1 from the right side (-1.1 to -1.0001), the slopes are approaching to -4. The value of the slope at P(-1,4) is then m = -4.

Estimate the instantaneous rate of change of h (t) = 2t² + 2 at the point t = −1. in other words, c

Answer from: Quest

v v cj van config k tbs eng r.c r.c fcb fb gb frfr

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Can someone pls ! pls answer all. no explanation needed..

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.

Answers: 1

Answer

Mathematics, 21.06.2019 22:40

What rotation was applied to triangle def to create d’e’f’?

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

In an equilateral triangle, each angle is represented by 5y+3. what is the value of y? a. 9.7 b. 10.8 c. 11.4 d. 7.2

Answers: 1

Answer

You know the right answer?

Estimate the instantaneous rate of change of h (t) = 2t² + 2 at the point t = −1.
in other wo...