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How do i do this graph question? Draw a suitable line? Help please!?
The line y=kx touches the curve y= x+(12/x) -5 at point Q. By drawing a suitable line on the same axes, use your graph to find the least value of k and coordinate of Q. Well , whats the suitable line that i need to draw? im stuck at that part. I ll draw the graph myself. Thank you in advance :)
1 Answer
- PuzzlingLv 76 years ago
Line y = kx is tangent to the curve y = x + (12/x) - 5.
Take the derivative of the curve.
y' = 1 + -12/x²
Let's set that for k:
y = (1 + -12/x²)x
y = x + -12/x
And we want that line to be the intersection of the curve and the line.
x + (12/x) - 5 = x - 12/x
Cancel x from both sides, and add 12/x to both sides:
12/x + 12/x - 5 = 0
24/x = 5
5x = 24
x = 24/5
x = 4.8
Plug in to get y:
y = 4.8 + 12/4.8 - 5
y = 4.8 + 2.5 - 5
y = 2.3
And the value for k:
y = kx
k = y/x
k = 2,3/4.8
k = 23/48
Source(s): https://www.desmos.com/calculator/wlfxaga1k5
