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    can someone tell me how to know if there is going to be an inflection on a curve just by looking at an equation. there was this question that asked me to sketch the curve, y=x^3+3 and i knew that it would be like wavy like --> /\/ but i didnt know that there was going to be an inflection.

    the whole idea of sketching curves scares me because substituting values is very time consuming in exams.
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    In this case, it's just a vertical translation of the graph y=x^3. Another way of telling is that when you differentiate you're left with a square, which means the only stationary point is at x=0, and differentiating again tells you that at this stationary point, \dfrac{d^2y}{dx^2}=0. This doesn't necessarily mean it's a point of inflection in general, but in the case of a cubic with just one stationary point, it does.

    For cubic graphs, there's no real way of noticing straight away whether it's going to have a point of inflection or not, unless you're good at differentiating and factorising quadratics in your head.
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    (Original post by nuodai)
    In this case, it's just a vertical translation of the graph y=x^3. Another way of telling is that when you differentiate you're left with a square, which means the only stationary point is at x=0, and differentiating again tells you that at this stationary point, \dfrac{d^2y}{dx^2}=0. This doesn't necessarily mean it's a point of inflection in general, but in the case of a cubic with just one stationary point, it does.

    For cubic graphs, there's no real way of noticing straight away whether it's going to have a point of inflection or not, unless you're good at differentiating and factorising quadratics in your head.
    so basically you're saying that if you differentiate it and you are left with, (something)^2, it means that its an inflection for cubic graphs?
    btw i wont need to know anything too advanced as i am only doing C1
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    (Original post by cooldudeman)
    so basically you're saying that if you differentiate it and you are left with, (something)^2, it means that its an inflection for cubic graphs?
    btw i wont need to know anything too advanced as i am only doing C1
    Yes, or indeed (something)×(something else)^2 + (something else again)

    Essentially, it has a point of inflection if it's a stretch/translation of the graph y=x^3. From your graph transformations stuff you should know that these are things like (x+a)^3 and kx^3 and so on; combining all the results together, the general rule is that anything of the form y=a(px+q)^3+b has a point of inflection. The only downside is that to be able to see whether not it has a point of inflection you have to check if it can be put in this form, which is a lot harder than completing the square!
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    (Original post by nuodai)
    Yes, or indeed (something)×(something else)^2 + (something else again)

    Essentially, it has a point of inflection if it's a stretch/translation of the graph y=x^3. From your graph transformations stuff you should know that these are things like (x+a)^3 and kx^3 and so on; combining all the results together, the general rule is that anything of the form y=a(px+q)^3+b has a point of inflection. The only downside is that to be able to see whether not it has a point of inflection you have to check if it can be put in this form, which is a lot harder than completing the square!
    oh okok thanks for your help!
 
 
 
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