Question

Test the function f(x)=x^5+x^3+x for symmetry​

Answer 1

f(x) = x^5 + x^3 + x

f'( x) = 5x^4 + 3x^2 + 1

f'(x) always positive Its increasing function

f( -x) = - (x^5 +x^3 + x)

odd function

f( 0) = 0

f''(x) = 20 x^3 + 6x

for postive x its positive

for negative x its negative

so slope increasing for +ve x so concave

for - ve its convex

see attachment graph