$\text { Determine the open intervals on which the graph of } f ( x ) = 3 x ^ { 2 } + 7 x - 3 \text { is concave }$ downward or concave upward.
A) concave downward on $( - \infty , \infty )$
B) concave upward on $( - \infty , 0 )$; concave downward on $( 0 , \infty )$
C) concave upward on $( - \infty , 1 )$; concave downward on $( 1 , \infty )$
D) concave upward on $( - \infty , \infty )$
E) concave downward on $( - \infty , 0 )$; concave upward on $( 0 , \infty )$

Question

$\text { Determine the open intervals on which the graph of } f ( x ) = 3 x ^ { 2 } + 7 x - 3 \text { is concave }$ downward or concave upward. 
A) concave downward on $( - \infty , \infty )$
B) concave upward on $( - \infty , 0 )$; concave downward on $( 0 , \infty )$
C) concave upward on $( - \infty , 1 )$; concave downward on $( 1 , \infty )$
D) concave upward on $( - \infty , \infty )$
E) concave downward on $( - \infty , 0 )$; concave upward on $( 0 , \infty )$

Quizplus · Accepted Answer

The concavity of a graph of a function is determined by the sign of its second derivative. For $f(x) = 3x^2 + 7x - 3$, the first derivative $f'(x) = 6x + 7$, and the second derivative $f''(x) = 6$, which is always positive. Therefore, the graph is concave upward on $(-\infty, \infty)$.

Determine the open intervals on which the graph of f(x)=3x2+7x−3 is concave \text { Determine the open intervals on which the graph of } f ( x ) = 3 x ^ { 2 } + 7 x - 3 \text { is concave } Determine the open intervals on which the graph of f(x)=3x2+7x−3 is concave

$\text { Determine the open intervals on which the graph of } f ( x ) = 3 x ^ { 2 } + 7 x - 3 \text { is concave }$