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?
A Maths method
Differeniate equation
dy/dx = 2x + 2/x^2
When dy/dx = 2, 2 = 2x +2/x^2
x= 1.46, draw tangent at 1.46
Emaths method
take your ruler, move along curve, and see which point on your curve will get tangent 2, is guess and check, i dun see any alternative
Originally posted by bonkysleuth: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).