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Math Help - tangentes

  1. #1
    Boo
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    tangentes

    Please:
    if
    f(x)=x^2-7x+6
    and
    g(x)= (x-1)(x^2+ax-2)

    a)for which a afre graphs of the f and g functions in the (1,0) intersect under the angle of pi/4?


    b) for which dots x tangent on graph of the function f in the point (x,f(x)) goes through the point (0,2)?

    Many thanks!
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  2. #2
    MHF Contributor

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    Re: tangentes

    Quote Originally Posted by Boo View Post
    Please:
    if
    f(x)=x^2-7x+6
    and
    g(x)= (x-1)(x^2+ax-2)

    a)for which a afre graphs of the f and g functions in the (1,0) intersect under the angle of pi/4?
    f'(x)= 2x- 7 and g'(x)= 1(x^2+ ax- 2)+ (x- 1)(2x+ a)= x^2+ ax- 2+ 2x^2+ (a- 2)x- a= 3x^2+ (2a- 2)x- (a+ 2)
    Those are, of course, the tangent of the angles they make with the x-axis: tan(\theta_f)= 2x- 7, tan(\theta_g)= 3x^2+ (2a-2)- (a+2).

    Now, use the trig identity tan(\theta_f- \theta_g)= \frac{tan(\theta_f)- tan(\theta_g)}{1- tan(\theta_f)tan(\theta_g)}


    b) for which dots x tangent on graph of the function f in the point (x,f(x)) goes through the point (0,2)?
    As I said, f'(x)= 2x- 7 so a tangent line, at (x_0, f(x_0)), through (0, 2) must be of the form y= (2x_0-7)x+ 2. Set (2x_0- 7)x_0+ 2= x_0^2- 7x_0+ 2 and solve for x_0

    [tex]Many thanks![/QUOTE]
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  3. #3
    Boo
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    Re: tangentes

    Hello, HallsofIvy!
    then I get :
    2x^2-7x+2=x^2-7x+2

    and then:
    x^2=0

    the result should be T1(2,-4) and T2(-2, 24)

    P.. HOw did U get x0 in latex?
    Many thanks!!!
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