For this question, we need what's called the Power Rule for derivatives. The rule says:Find dy/dx for:
A. y = x(cubed) - x(squared)
That is, to take the derivative of a variable raised to some power, we multiply by the power and then subtract one from the power to get the new power. now let's see how this applies to your question
.......we usually skip this step, but i just wanted to show you the rule in action
this is more complicated. now you can expand everything and use the power rule, but if you want to look sophisticated you would use what is called the Product Rule on this one.B. y = (x-1) (x+2)
The Product Rule says:
If we have the product of two functions, say f(x) and g(x), and we want to take the derivative of this product, it will be the derivative of the first function times the second added to the derivative of the second function times the first. That is,
Now let's see this rule in action.
i'll let you practice with this one. I will give you this hint. Turning points occur whenFind the turning points for the following and state what type of turning points they are:
C. y = x(cubed) - 3x + 2
afterwards, we find , that means the second derivative. you just take the derivative of the function.
Then we plug in the x's we found from setting into this new function. and we can tell what the turning point is by the following:
The turning point is a local maximum if we get when we plug in a critical value (that is the value that makes dy/dx = 0)
The turning point is a local minimum if we get when we plug in a critical value
The turning point is POSSIBLY an inflection point if we get when we plug in a critical value. Further tests are usually needed in this case.
I've never seen anyone ask a Psychology question here, so you might not get to help anybody, just letting you knowI'm doing a psychology course (believe it or not), so if anyone needs any help with that sort of stuff, I'm more than happy to help.
if you have any questions, don't hesitate to ask