Question

which of the following is true about the function g(x)= 4x^2 - 3x^4?

a)g is decreasing for x<1
b) g has a relative extreme value at (0,0)
c)the graph of g is concave up for all x<0

Answer 1

g' = 8x-12x^3 = 4x(2-x^2)
g" = 8-36x^2

g' changes sign in x<1, so not (a)
g'=0 and g"≠0 at x=0, so (b)
g" changes sign, so not (c)

so, (b) is the only true statement

Answer 2

the answer is a

Answer 3

g'(1/2) = 4(1/2)(2-1/4) = 2(7/4) = 7/2
So, g is increasing at x = 1/2

Have you looked at the graph?

http://www.wolframalpha.com/input/?i=4x^2+-+3x^4

Clearly only (b) is true