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# Extrema

How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

# 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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