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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.

# Inflection Points

Given the function $$f(x)=3x^3-9x^2+14x+36,$$ what is the inflection point $$(a,b)$$ of $$f(x)$$?

If one of the inflection points of the curve $y = \ln (ax^2 + b)$ is $$(1, \ln 50)$$, what is the value of $$a \times b$$?

Let $$f(x)=x^3+12x^2+3x-5.$$ If $$a$$ and $$b$$ are constants such that the inflection point of the curve $$y=f(x-a)+b$$ is the origin $$(0,0),$$ what is the ordered pair $$(a,b)?$$

If $$a$$ and $$b$$ are constants such that the curve $f(x)=\ln (ax^2 + b)$ has an inflection point $$(1,\ln 16),$$ what is the value of $$ab?$$

The slope of the tangent line to the curve $y=ax^3-bx^2+cx$ at $$x=2$$ is $$13,$$ where $$a, b$$ and $$c$$ are constants. If $$P=(1,7)$$ is the inflection point of the curve, what is the value of $$a+b+c$$?

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