Derivatives Affecting Shape of the Graph

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To analyze the function h(x) = (x^2-1)^3, the first step is to find its derivative to determine intervals of increase or decrease. A function is increasing where its derivative is positive and decreasing where the derivative is negative. After identifying these intervals, local maximum and minimum values can be found by evaluating critical points. Additionally, the intervals of concavity and inflection points can be determined using the second derivative. Understanding these concepts is essential for accurately sketching the graph of the function.
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I have the following question:

h(x) = (x^2-1)^3

a) Find the intervals of increase or decrease
b) Find the local maximum and minimum values
c) Find the intervals of concavity and the inflection points
d) Use the informatin from parts (a)-(c) to sketch the graph

Now I figure a good way of starting this question is just to graph it to begin with anyways. However, the first step really is to find the derivative (f') of this function if I am not mistaken. However, can anyone explain to me how you would go about finding the intervals of increase or decrease for this function. From there, I can figure out the rest. That's all, thanks guys.
 
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Well, what does it mean that a function is increasing?
And how may you ascertain where a differentiable function is increasing?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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