Homework Soursefx 13x3 52x2 4x 6 aFind the coordinates of the critical poi
f(x)= 1/3(x)^3 + 5/2(x)^2 +4x -6
a)Find the coordinates of the critical points
b)Determine if each critical point is a local ma or min, using the 1st or 2nd derivative test. Provide both x and y coordinates for extrema.
c)find x and y coordinates for the points of inflection
a)Find the coordinates of the critical points
b)Determine if each critical point is a local ma or min, using the 1st or 2nd derivative test. Provide both x and y coordinates for extrema.
c)find x and y coordinates for the points of inflection
Solution
f(x) = 1/3(x)^3 + 5/2(x)^2 +4x -6
take derivaitve
f\'(x) = x^2 + 5x+4 = 0
(x+1)(x+4) = 0
x = -1 or -4
take second derivaitve
f\'\'(x) = 2x+5
at x = -1 f\'\'(-1) = 5-2 = 3 > 0
at x= -1 it has minima
at x =2
f\'\'(-4) = 5-2*4 = 5-8 = -3 < 0
at x= -4 it has maxima
x = -1 and -4 are inflection points
