Calculus
Extrema
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 \(a-b?\)