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Please help me with this 3-part question (Differential Calculus:Rules for differentiation):
Q1) Find the coordinates of the points on the curve y=x²-5x+6 at which the tangent:
A) makes an angle of 45 degrees with the X-axis.
B) is parallel to the line with the equation 3x+y-4=0
C) is perpendicular to the line with the equation 2y-x+3=0
Thanks in advance
Last edited by 12334545 (2007-08-03 16:48:57)
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Please help me with this 3-part question (Differential Calculus:Rules for differentiation):
Q1) Find the coordinates of the points on the curve y=x²-5x+6 at which the tangent:
A) makes an angle of 45 degrees with the X-axis.
B) is parallel to the line with the equation 3x+y-4=0
C) is perpendicular to the line with the equation 2y-x+3=0Thanks in advance
Well, as a rule whenever I see "at which the tangent" I find y'
y=x²-5x+6
y'=2x - 5
When a line makes an angle of 45 degrees with the x axis it has a slope of 1 (tan45 = 1)
so y' must be 1
2x - 5 =1
x = 3
plugging that into the original question we get that y = (3)² -5(3) +6 = 0
so A) (3,0)
B) the line 3x+y-4 = 0 or
y = -3x + 4
has a slope of -3. Now repeat the above steps:
y' = -3 = 2x - 5
x=1
and
y = 2
B) (1,2)
The line 2y-x+3=0 or (y = .5x - 1.5)
The slope of a perpendicular is the opposite reciprocal so y' = -2
Blah, blah, blah and so on.
C) (1.5,.75)
Last edited by bossk171 (2007-08-03 17:19:24)
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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Thanks soo much. Fast response too!
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