Question

if f(x)= 4x^3-21x^2+36x-4, then the graph of f is decreasing and concave up on the interval(?,?)

Answer 1

i got (3/2,2) but wasn't sure

Answer 2

f = 4x^3-21x^2+36x-4
f' = 12x^2 - 42x + 36 = 6(2x^2-7x+6) = 6(2x-3)(x-2)
f" = 24x-42 = 6(4x-7)

f is concave up for x > 7/4
f is decreasing for x in (3/2,2)

So, both for x in (7/4,2)

f has a max at x=3/2, so it cannot be concave up there.

Answer 3

ok ty!