Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x^
ID: 2864677 • Letter: C
Question
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x^4 - 8x^2 + 5 Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) Find the local minimum and maximum values of f. local minimum value local maximum value Find the inflection points. (x, y) = (smaller x-value) (x, y) (larger x-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)Explanation / Answer
given f(x)=x4-8x2+5
differentiate
f '(x)=4x3 -16x
differentiate
f "(x)=12x2 -16
for inflection point f "(x)=0
12x2 -16=0
x2 =16/12
x2 =4/3
x =(-2/3) , x =(2/3)
f(-2/3)=(-2/3)4 -8(-2/3)2+5=-35/9
f(2/3)=(2/3)4 -8(2/3)2+5=-35/9
inflection points are (-2/3, -35/9),(2/3, 35/9)
concave up when f "(x)>0
12x2 -16>0
x2>4/3
x=(-,-2/3)U(2/3 ,)
concave DOWN when f "(x)<0
12x2 -16<0
x2<4/3
x=(-2/3 ,2/3)