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

would you like the choices?

Answer 2

a. (3/2, 2)
b. (neg. infinity, 7/4)
c. (7/4, infinity)
d. (7/4, 2)
e. (3/2, 7/4)

Answer 3

A plot is attached

Answer 4

Given f(x)= 4x^3-21x^2+36x-4.
The graph is decreasing when f'(x)<0.
f'(x)=12x^2-42x+36
which factors into f'(x)=6(x-2)(2x-3).
This means that f'(x) is negative (f(x) decreasing) between 1.5 and 2, or (1.5,2).
For concavity, we look at f"(x)=24x-42=6(4x-7), which means that
f(x) is concave up when x>7/4, or (7/4,+inf)
Therefore f(x) is increasing and concave up between 7/4 and 2, or (7/4,2)

Answer 5

ah thank youu!!