calculus

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find the point(s) on the graph of y = (2x4 + 1)(x - 5) where the tangent line slope is 1.

  • calculus -

    I assume you meant
    y = (2x^4 + 1)(x - 5)

    using the product rule

    dy/dx = (2x^4+1)(1) + 8x^3(x-5)
    simplify and set it equal to 1 gives me
    2x^4 + 1 + 8x^4 - 40x^3 = 1
    10x^4 - 40x^3 = 0
    10x^3(x-4) = 0
    so x = 0 or x = 4

    those are the x's of your two points where the slope of the tangent is 1
    sub into the origianal to get the y's

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