Calculus problem?

Question

Suppose f(x) = 3x4. Does f have an inflection point for x in the interval (0,1)? If so, enter its x coordinate

Answer 1

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To find the POI, you have to set the seconds derivative equal to 0.

f(x) = 3x^4

f'(x) = 12x^3

f'(x) = 36x^2

36x^2 = 0

x=0

sub in values from both sides in the second derivative equation

f''(-1) = +

f''(1) = +

Really because the x value is squared, it can't be anything but positive. Because it is positive on both sides of the value found, there is no POI.

Answer 2

is that 3x^4?

f'=12x^3

f"=36x^2

x=0