Hi
I'm having trouble finding the turning point(max & min) of this equation and also the stationary points and x-intercepts.
$\displaystyle y=9(x-1)^2-(x-1)^4$
P.S
The x-intercepts are the points where the curve hits the x-axis. Do you mean you have trouble solving $\displaystyle f(x) = 0$ for $\displaystyle x$ ?
Think about using the derivative. When the derivative is $\displaystyle 0$ in a point, the function is very likely to turn round at this point (although sometimes it doesn't).
Steps :
- get the derivative $\displaystyle f'(x)$ of your function $\displaystyle f(x)$
- solve for $\displaystyle x$ with $\displaystyle f'(x) = 0$
- ensure each point found is indeed a turning point (you should know how to do this last step)
Does it make sense ?