What is the turning point for f(x) = –x^4 – 4 ?

Question

What is the turning point for   f(x) = –x^4 – 4   ?

campbell_st · Answer

the curve is concave down. 

and is symmetric about the y-axis.

so the y-intercept will be the turning point. 

the alternative method is to use calculus. 

f'(x) = - 4x^3  

let f'(x) = 0

so a stationary point existed at x = 0

f''(x) = -12x^2

test the stationary point in the 2nd derivative to determine its nature.

anonymous · Answer

wait, how and why´d you do this f'(x) = - 4x^3 ?

campbell_st · Answer

do you know how to differentiate

anonymous · Answer

no

anonymous · Answer

i was able to solve for this though, (x+3)^3

anonymous · Answer

how is this different?

campbell_st · Answer

ok... then do you know how to find the axis of symmetry of a curve...?

campbell_st · Answer

oops of a parabola

anonymous · Answer

what?

campbell_st · Answer

just interested in how you used a cubic function to find the turning point in a quartic function. 

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and then there is your curve

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