Quandaries
and Queries 

hi, my name is Louise. i am a senior in high school taking Ap calculus and i have a problem i need help answering. it would be greatly appreciated the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is A. y = 12x + 8 B. y = 12x + 40 C. y + 12x  8 D. y = 12x + 12 E. y = 12x  40 

Hi Louise, If there is a point of inflection on this curve then it must be at a point where the second derivative is zero. Hence I found the first and second derivatives
Thus the second derivative is zero if x = 2. At x = 2 the value of the first derivative is
Thus the tangent line is the line with slope 12 and through the point on the curve with x = 2. Penny 

