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**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

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)

But the answer given is (0,1),(1,-6)and (-1,8). Is the answer correct?