Calculus

# Second Derivative Test

What is the sum of all the local minima of $f(x)=3x^4-8x^3-6x^2+24x+14?$

Let $y=ax+b$ be a line that intersects the curve $f(x)=x^3-x$ at three points including its inflection point. Let $c, d$ and $e$ be the $x$-coordinates of the three intersection points with $c If $f'(c)=5,$ what is $f'(e)?$

How many inflection points does the curve $y=2xe^{-x^2}+7$ have?

What is the minimum value of integer $a$ such that the curve $y=7x^4-5x^3+ax^2$ has no inflection points?

Let $a$ and $b$ be the local maximum and local minimum of the function $f(x)=-x^3+9x^2+13,$ respectively. What is the value of $a-b?$

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