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Calculus

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The curve f(x)=-x^4+2x^2+x has a tangent at the point (1,2). Is this line tangent to the curve at another point and, if so where?

  • Calculus -

    dy/dx = 4x^3 + 4x + 1
    so at (1,2) dy/dx = 4+4+1 = 9

    so is 4x^3 + 4x + 1 = 9 ?
    x^3 + x - 2 = 0
    we already know that (x-1) is a factor, so by synthetic division I found
    x^3 + x - 2 = 0
    (x-1)(x^2 + x + 2) = 0
    x = 1, we knew that or
    x = (-1±√-7)/2 which is not real

    so there are no other points where the tangent has a slope of 9

  • Calculus -

    find the tangent line, graph both of them

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