Ask Experts Questions for FREE Help !
Ask
    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #1

    Sep 5, 2007, 03:13 AM
    Differentiation topic
    Hi there,
    Differentiation can be a most confusing topic.

    How would do this question below:

    The angle of inclination of a tangent to the curve y=x^2-5x+1 is 45 DEGREES. Determine the coordinates of the point where the tangent touches the curve.

    Could you please show me a step by step solution to do this as I'm new at this topic

    Thanks
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
    Uber Member
     
    #2

    Sep 5, 2007, 04:10 AM
    45 degrees is equivalent to a derivative of 1. (because the line x = y has slope 1 and is 45 degrees)

    So, you need to differentiate and set dy/dx as 1. and solve for x, then you can get back y.
    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #3

    Sep 5, 2007, 04:17 AM
    Sorry I don't quite understand the differentiate and set it as dy/dx part
    I've learn't dy/dx is another symbol for the differentiated form but I'm still confused
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
    Uber Member
     
    #4

    Sep 5, 2007, 04:27 AM
    dy/dx basically means "differential of y with respect to x".

    Say i had the equation x^2 and wanted to find the 45 degree tangent point just like you do.

    I calculate the derivative:




    since I want to find the point where





    so from the original equation:







    So the point where y=x^2 has a 45 degree tangent is (0.5,0.25)

    Does that make any more sense?
    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #5

    Sep 5, 2007, 04:33 AM
    Thank you Capuchin, it makes more sense now
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
    Uber Member
     
    #6

    Sep 5, 2007, 04:35 AM
    Please ask if you have further questions.

    Calculus is an incredibly powerful tool but can take some time to get your head around.

    Let me know what you get for an answer.
    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #7

    Sep 5, 2007, 04:55 AM
    I believe the points are (3,-5)
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
    Uber Member
     
    #8

    Sep 5, 2007, 05:03 AM
    That's what I got too, well done :)

    You can always plot the graph and check that the tangent is 45 degrees at that point. I think that this is a very good idea when you are learning calculus, as it can sometimes seem very abstract.
    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #9

    Sep 5, 2007, 05:07 AM
    I have another confusing question but I'll try to figure it out myself before I ask you again.

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Trig differentiation [ 4 Answers ]

I'm having a problem differentiating y=2sin(t)^2 I get 4sin(t)*2cos(t) but this is wrong any ideas on how to do it right

Implicit differentiation [ 2 Answers ]

Use implicit differentiation to find y' ln(xy) = x+y Use implicit differentiation to find y' at (5,2) 3xy + 3x = 45 Find the differential dy given the following function if p and q are constants f(x) = x^p + x^q

Implicit differentiation [ 10 Answers ]

Use implicit differentiation to find y' : xe^xy=y Use implicit differentiation to find y': xln y = y^3 - 2

Implicit Differentiation [ 1 Answers ]

The question is as follows: Recall that (x-h)^2 + (y-k)^2 = r^2. The circle's center is (h,k), with radius r. Show that the tangent (derivative) to is perpendicular to the radius at the point of tangency. Use implicit differentiation. If anyone could help me with that question...

Calculus implicit differentiation [ 1 Answers ]

The equation 4x^2y - 3y = x^3 implicitly defines y as a function of x. a) use implicit differentiation to find dy/dx. b) write y as an explicit function of x and compute dy/dx directly. Show that the results of parts a and b are equivalent. I don't know how to show that they are...


View more questions Search