The variables x and y are connected by the equation y = x^2 +
2/x
The table below shows some values of x and the corresponding
values of y
x -3 -2
-1 -0.5
-0.1
0.1
0.5 1 2
y 8.33 3 -1
-3.75 -19.99
20.01 4.25
3 5
By drawing a tangent, find the x-coordinate of the point P at
which the gradient of the curve y = x^2 + 2/x at P is 2
How do you know where to draw the tangent?
For me, I looked at the parts of the graph which is increasing.
There are only 2 regions: between -0.1 to 0 and between 1 and
2.(the range of graph we were told to draw)
so i roughly drew a tangent at these 2 regions and found that x
is about 1.5. Is there another way to do this without having to
"guess" the answer?
Steps :
(1) Since the gradient of the tangent is 2, we will
draw the line y=2x
(2) Use two rulers, just the way 2 parallel
lines are drawn.
Shift the line y=2x in
parallel until it just touches the curve
This line that just
touches the curve will intersect the curve at about x =
1.5
(exact x value = 1.46).