Calculus

Extrema

Concave / Convex Functions

         

What is the inflection point of the curve y=x33x2+7x+12?y=x^3-3x^2+7x+12?

What is the maximum value of real number aa such that the curve y=x2(lnx13)y=x^2(\ln x-13) is concave down in the interval (0,a)?(0,a)?

If f(x)=ln(x2+9) f(x) = \ln (x^2 + 9) , the interval on which the curve y=f(x) y = f(x) is concave up can be expressed as a<x<b a < x < b . What is the value of ba b - a ?

If f(x)=x432x3+288x2+8x15 f(x) = x^4 - 32 x^3 + 288 x^2 + 8x - 15 , the interval on which the curve y=f(x) y = f(x) is concave down can be expressed as a<x<b a < x < b . What is the value of a+b a + b ?

Let f(x)=x440x3+504x2+19x+17f(x) = x^4 - 40 x^3 + 504x^2 + 19x + 17. Given that f(x)f(x) is concave in the domain [a,b]\left[a,b\right], what is the value of a+ba+b?

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