Calculus

Extrema

Inflection Points

         

Given the function f(x)=3x39x2+14x+36,f(x)=3x^3-9x^2+14x+36, what is the inflection point (a,b)(a,b) of f(x)f(x)?

If one of the inflection points of the curve y=ln(ax2+b) y = \ln (ax^2 + b) is (1,ln50) (1, \ln 50) , what is the value of a×b a \times b ?

Let f(x)=x3+12x2+3x5.f(x)=x^3+12x^2+3x-5. If aa and bb are constants such that the inflection point of the curve y=f(xa)+by=f(x-a)+b is the origin (0,0), (0,0), what is the ordered pair (a,b)?(a,b)?

If aa and bb are constants such that the curve f(x)=ln(ax2+b)f(x)=\ln (ax^2 + b) has an inflection point (1,ln16),(1,\ln 16), what is the value of ab?ab?

The slope of the tangent line to the curve y=ax3bx2+cxy=ax^3-bx^2+cx at x=2x=2 is 13,13, where a,ba, b and cc are constants. If P=(1,7)P=(1,7) is the inflection point of the curve, what is the value of a+b+ca+b+c?

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