For what values of x is #f(x)= x^4-3x^3-4x-7 # concave or convex?

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Answer 1 · 2017-02-12T07:29:44

the function is convex in #]-oo;0[uu]2/3;+oo[# and concave in #]0;2/3[#

You would analyze the second derivative; the first one is:

#f'(x)=4x^3-9x^2-4#

then the second one is:

#f''(x)=12x^2-18x#

Let's solve the inequality #f''(x)>0#:

#12x^2-8x>0#

that's

#x<0 or x>2/3#

Then the given function is convex in

#]-oo;0[uu]2/3;+oo[#

and concave in

#]0;2/3[#

graph{x^4-3x^3-4x-7 [-5, 5, -27, 10]}