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Second Derivative Test


What is the sum of all the local minima of f(x)=3x48x36x2+24x+14?f(x)=3x^4-8x^3-6x^2+24x+14?

Let y=ax+by=ax+b be a line that intersects the curve f(x)=x3xf(x)=x^3-x at three points including its inflection point. Let c,dc, d and ee be the xx-coordinates of the three intersection points with c<d<e.c<d<e. If f(c)=5,f'(c)=5, what is f(e)?f'(e)?

How many inflection points does the curve y=2xex2+7y=2xe^{-x^2}+7 have?

What is the minimum value of integer aa such that the curve y=7x45x3+ax2y=7x^4-5x^3+ax^2 has no inflection points?

Let aa and bb be the local maximum and local minimum of the function f(x)=x3+9x2+13,f(x)=-x^3+9x^2+13, respectively. What is the value of ab?a-b?


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