F is increasing if f '(x) = 4x^3<span> - 64x >0, so it is the same of x(x^2 -16)>0, implies x>0 or (x-4)(x+4)>0, so x> + or -4 the answer is </span><span>(-4 , 0) ∪ (4 , infinity)
</span>f is decreasing if f '(x) = 4x^3 - 64x <0, so it is the same of x(x^2 -16)<0, implies x<0 or (x-4)(x+4)<0, so x< + or -4 the answer is (- infinity, -4) ∪ (0 , 4)
<span>the local minimum and maximum </span>f '(x) =0, impolies x=+ or -4, or x=0 or f'(o)=0, and f'(- 4)=f'(4)= 0, M(-4, 0) or M(4, 0) or M(0,0)
<span>inflection points can be found by solving f '' (x)=12x^2 - 64 =0 </span>x=+ or - 4sqrt(3) / 3 so the inflection point is and M(- 4sqrt(3) / 3, f'' ( -4sqrt(3)) (smaller x value), and M(4sqrt(3) / 3, f'' (4sqrt(3)) (larger x value)
f is concave up if f ''>0 it means 12x^2 - 64>0, so the interval is (- infinity, -4sqrt(3) U (4sqrt(3), infinity)
f is concave down if f ''<0 it means 12x^2 - 64<0 so the interval is (-4sqrt(3)) U (4sqrt(3))
I beliive it is 16, but haven't done this in a bit haha
Step-by-step explanation:
So bisect means to "split in half" aka segment BD is directly in the middle of triangle ABC. This means we can look at the half of the triangle we know (ABD). We see a 16, so therefore x should be 16.