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math grade 11

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A quadratic function is defined by
f(x)= 3x^2+4x-2. A linear function is defined by g(x)= mx-5. what values(s) of the slope of the line would make it a tangent to the parabola.

  • math grade 11 - ,

    Slope of any function is first derivate of that function.

    Quadratic function in your case have first dervate:

    3*2*x+4=6*x+4

    Linear function in your case have first dervate:

    m

    Line will be tangent of quadratic parabola when first derivates is egual.

    m=6*x+4
    m*x-5=(6*x+4)*x-5=6*x^2+4*x-5

    3*x^2+4*x-2=6*x^2+4*x-5
    3*x^2+4*x-6*x^2-4*x=-5+2
    -3*x^2=-3 Multiply with (-1)
    3*x^2=3 Divided with 3
    x^2=1
    x=+OR-(1)
    x1=-1 , x2=1

    Slope for x1=6*x1+4=6*(-1)+4=-6+4=-2

    Slope for x2=6*1+4=6+4=10

    S1=-2 S2=10

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