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 $$c<d<e.$$ 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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