Please answer the following questions about the function f(x) = 3x65-2x^4. Instr
ID: 2872900 • Letter: P
Question
Please answer the following questions about the function f(x) = 3x65-2x^4. Instructions if you are asked to find x- or y-values enter either a number a list of numbers separated by commas or None if there aren't any solutions. Use interval notation if you are asked to find an union of intervals and either {} if the interval is empty Find the critical numbers of f where it is necessary and decreasing and its local extrema. Find where f is concave down and has infection points. Find any horizontal and vertical asymptotes of f The function f is
Explanation / Answer
f(x)=3x5-2x4
a)f'(x)=3*5x4-2*4x3=0
==>15x4-8x3=0
==>x3(15x-8)=0
==>x=0, 15x-8=0
==>x=0,x=8/15
increasing ==>f'(x)>0 ==>x3(15x-8)>0==>(-inf,0)U(8/15, inf)
decreasing ==>f'(x)<0 ==>x3(15x-8)<0==>(0,8/15)
f"(x)=15*4x3-8*3x2=60x3-24x2
f"(0)=0==>local maxima
f"(8/15)=60(8/15)3-24(8/15)2=32(8/15)2 >0==> local minima at x=8/15
b)concave up
f"(x)=60x3-24x2>0==>12x2(5x -2)>0==>x>2/5==>x>0.4
x=(0.4,inf)
concave down
f"(x)=60x3-24x2<0==>12x2(5x -2)<0==>x<2/5==>x<0.4
x=(-inf,0.4)
inflection points
f"(x)=60x3-24x2=0==>12x2(5x -2)=0==>x=2/5
x=2/5=0.4
c)no horizontal or vertical asymptotes
d)f is continous because it is defined for all x in domain of f.
no symmetry