Graph sketch problem involves this function: (2ax ^ 2-x ^ 3) ^ (1 ÷ 3)
- Thread starter Magno
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What is the definition of concavity?
Yes I considered the second derivative however I can not determine the roots of the function.
mmm4444bot
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You typed spaces around the carot symbols, but not around the subtraction operator.
Some people use such spacing to denote grouping, so let's be sure we're looking at the same function. I'm reading it as:
\(\displaystyle f(x) = \sqrt[3]{2 \cdot a \cdot x^2 - x^3}\)
That is:
f(x) = (2ax^2 - x^3)^(1/3)
We cannot graph a function that contains an unknown parameter. If you do not have any information about symbol a, then I would suggest taking cases (a<0, a=0, a>0) and see what happens.
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Technically, this is not a "function"; it's not even an "equation", because there's no "equals" sign in it. Is this supposed to be "y=", or "f(x)=", or something similar?
Also, the expression is unclear. Are you given a value for "a"? Is the expression (other than the cube-root part) equal to any of the following?
. . . . .\(\displaystyle \mbox{a. }\, 2ax^2\, -\, x^3\)
. . . . .\(\displaystyle \mbox{b. }\, (2ax)^2\, -\, x^3\)
. . . . .\(\displaystyle \mbox{c. }\, 2ax^{2 - x^3}\)
. . . . .\(\displaystyle \mbox{d. }\, 2ax^{(2 - x)^3}\)
Or something else?
When you reply, please include a clear listing of your thoughts and efforts so far, such as your work in finding the first and second derivatives. Thank you!
