Calculus
posted by Bill on .
What is the point of inflection of the function f(x)=x^38x^2+5x+50? Is the local extrema at f(1/3)=50.8 max and f(5)=0 min?
For the second derivative I got f(x)=6x16 and then got x=16/6 when set to zero.

3 x^2 16 x + 5 = 0
first derivative
at x = {16 +/sqrt(25660)]/6
or [16+/14]/6 = 5 or 0.3333
second derivative
6 x  16
is that + or  at the two points where the slope is zero?
at x = .333
2  16 is negative so maximum there
at x = 5
6x  16 = 3016 is positive so minimum there