Turning Points


Given the function \( f(x) = \frac{ x^2-8x + 12}{x^2+6x - 16} \), what is \(\displaystyle{\lim_{ x \rightarrow 2 } f(x)} \)?

How many integers \(k\) are there such that the function \[f(x)=x^3+kx^2+3x+2\] has no turning points?

Let \(f(x)=x^3-6x^2+14x+9.\) What is the sum of the \(x\)-coordinates of turning points such that \(f(x)\) switches from a decreasing function to an increasing function?

A polynomial of degree \(25\) has \(m\) real roots and \(n\) turning points. What is the maximum value of \(m+n\)?

What is the sum of all the \(x\)-coordinates of the turning points in the graph of \[f(x)=-2x^3+18x^2-30x+9?\]


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