Inflection Points of f(x) = x^4 - 10x + 7

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Malga1968

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Oct 15, 2007
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If f(x) = x^4-10x+7

How would i find the point of inflection.

I started off with getting the second derivative:

First Derivative: 4x^3-10
Second Derivative: 12x^2

But dont know where to go from here to find my points of inflection.

Any help would be greatly appreciated.

Malga
 
inflection points occur where f(x) is defined and f''(x) changes sign.
 
set f''(x) = 0 ...

12x^2 = 0

solve for x ...

x = 0

since f(0) = 7, f(x) is defined at x = 0.

now, does f''(x) change sign at x = 0?

if it does, then there is a point of inflection at x = 0.

if it doesn't, then there is no point of inflection at x = 0.
 
skeeter said:
set f''(x) = 0 ...

12x^2 = 0

solve for x ...

x = 0

since f(0) = 7, f(x) is defined at x = 0.

now, does f''(x) change sign at x = 0?

if it does, then there is a point of inflection at x = 0.

if it doesn't, then there is no point of inflection at x = 0.
Click to expand...

Thanks for providing me with more help. Would my inflection points be (0,7)... Or am I really missing the point here? Its been 15 years since my last math course, I took Algebra II.
 
you are missing the point.

for values of x < 0, 12x^2 is positive. for values of x > 0, 12x^2 is still positive.

so, f''(x) does not change sign at x = 0.

your function has no inflection points.
 
skeeter said:
you are missing the point.

for values of x < 0, 12x^2 is positive. for values of x > 0, 12x^2 is still positive.

so, f''(x) does not change sign at x = 0.

your function has no inflection points.
Click to expand...

I guess my age is setting in. Thank you Skeeter.
 
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