Inflection points? Does f(x) = 2x ?10x +20x +x+1 have any inflection points? If so, identify them.

Solution Step 1 In this problem we have to find the inflection point of f(x) = 2x 10x + 20x + x + 14 3 First let us see the definition of inflection points. Inflection Point: An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. A necessary condition for x to be an inflection point is f (x) = 0 3 For example, In the curve y = x plotted below, the point x = 0is an inflection point . Step 2 5 4 3 Let f(x) = 2x 10x + 20x + x + 1 By the definition given in step 1, in order to find the inflection points, we have to differentiate the function twice and then equate it to zero that is f (x) = 0