# Fuction and Graph

1. Homework Statement
The function f is defined as
f(x)=3x^5-10x^3+1
1) Determine the maximum and minimum points, as well the point of inflection of the graph f.

2. Homework Equations
All the differentiation equation.

3. The Attempt at a Solution

I found the maximum point and minimum point, but I had some trouble with the inflection point.

So....
f''(x)=60x^3-60x^2
f''(x)=0,
60x^3-60x^2=0
x=0, x=1

f'''(0)=0

Hence the only inflection point is (1,-6)

Related Precalculus Mathematics Homework Help News on Phys.org
Not sure this should be in this topic as it is calculus not precalculus.

Have another look at your differentiation, in particular check the term -60x^2 in your expression for f''(x).

f''(x)=60x^3-60x^2
This second derivative is wrong. Calculate it again.

marlon

HallsofIvy
Homework Helper
1. Homework Statement
The function f is defined as
f(x)=3x^5-10x^3+1
1) Determine the maximum and minimum points, as well the point of inflection of the graph f.

2. Homework Equations
All the differentiation equation.

3. The Attempt at a Solution

I found the maximum point and minimum point, but I had some trouble with the inflection point.

So....
f''(x)=60x^3-60x^2
f''(x)=0,
60x^3-60x^2=0
x=0, x=1

f'''(0)=0

Hence the only inflection point is (1,-6)