What are the points of inflection, if any, of f(x) =-3x^3 - 7x^2 + 3x?

1 Answer
Jun 5, 2017

The point of inflection is =(-0.778,-5.156)#

Explanation:

We calculate the first and second derivatives

f(x)=-3x^3-7x^2+3x

f'(x)=-9x^2-14x+3

f''(x)=-18x-14

The point of inflection is when

f''(x)=0

-18x-14=0, =>, x=-14/18=-7/9

Therefore, the point of inflection is

(-7/9, f(-7/9))=(-0.778,-5.156)

We can build a chart

color(white)(aaaa)xcolor(white)(aaaa)(-oo, -7/9)color(white)(aaaa)(-7/9,+oo)

color(white)(aaaa)f''(x)color(white)(aaaaaa)+color(white)(aaaaaaaaaaaaa)-

color(white)(aaaa)f(x)color(white)(aaaaaaaa)uucolor(white)(aaaaaaaaaaaaa)nn
graph{(y-(-3x^3-7x^2+3x))((x+0.778)^2+(y+5.156)^2-0.01)=0 [-11.24, 6.54, -8.084, 0.805]}