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Math Help - concavity

  1. #1
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    concavity

    find dy/dx and d^2/dx^2. for which values of t is the curve concave upwards?

    x=2sint
    y=3cost
    0<t<2pi

    i got (-3/4)sec^3t as d^2/dx^2. you need that to find the concavity right? but how do you do it?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jeph View Post
    find dy/dx and d^2/dx^2. for which values of t is the curve concave upwards?

    x=2sint
    y=3cost
    0<t<2pi

    i got (-3/4)sec^3t as d^2/dx^2. you need that to find the concavity right? but how do you do it?
    A function with second derivative is concave upwards on any interval
    where the second derivative is >=0

    RonL
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  3. #3
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    Hello, jeph!

    Find dy/dx and d/dx.
    For which values of θ is the curve concave upwards?

    x = 2sinθ, .y = 3cosθ, .0 < θ < 2π

    i got: .dy/dx = -secθ . Good!

    You need that to find the concavity, right?
    But how do you do it?

    As the Captain pointed out, the curve is concave up when dy/dx is positive.

    So you need to solve this inequality: .-secθ .> .0
    . . I'll take baby-steps . . .

    Divide by -: .secθ .< .0

    Take cube roots: .secθ .< .0

    When is secθ negative?
    . . When is 1/cosθ negative? .In Quadrants 2 and 3.

    Hence, the curve is concave up for: .π/2 < θ < 3π/2

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  4. #4
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    thanks guys! i guess that - sign got me a little confused...the < and > signs only switch when you are dividing or multiplying a negative right? these small things always slip out of my mind.....
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