Question

A and B are the points on the curve y=2^x with the coordinates 3 and 3.1 respectively.

Find the gradient/slope of the chord AB and stating the points you use, find the gradient of another chord which will give a closer approx. to the gradient/slope of the tangent to y=2^x at A.

thanks

Answer 1

A = (3, 2^3) = (3,8)

B = (3.1,2^(3.1)) = (3.1, 8.57)

slope = .57/.1 = 5.7

Answer 2

since a is at 3; use a closer value of x that is between 3 and 3.1; such as 3.01

Answer 3

as you get closer and closer to A, which is (3,8); you will approach the limit that is equal to the slope at 'A'; also known as the derivative of y = 2^x at x=3

Answer 4

does that help?

Answer 5

wait let me read it through a few times :S

Answer 6

how did you get the slope?
where did you get the numbers from 0.57/0.1=5.7???

Answer 7

you are given a function for y: 2^x correct?

At point A it says that x=3

and at point B, x=3.1 right?

Answer 8

yes

Answer 9

point A = (3,2^3)

point B = (3.1, 2^(3.1))

Answer 10

B-A gives you the slope:

x , y
--------------
3.1 , 2^(3.1)
-3 , - 2^3
---------------
( .1 , .57418...)

slope = y/x = .57/.1 = 5.7/1 = 5.7

Answer 11

thanks

Answer 12

youre welcome :)