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12334545

Member

Registered: 2007-04-02

Posts: 5

Need Help With One Question

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)

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Need Help With One Question

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

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)

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

12334545

Member

Registered: 2007-04-02

Posts: 5

Re: Need Help With One Question

Thanks soo much. Fast response too!