Determine the open intervals on which the graph of $f ( x ) = 2 x ^ { 2 } + 5 x - 4$ is concave downward or concave upward.
A)concave upward on $( - \infty , 0 )$ ; concave downward on $( 0 , \infty )$
B)concave downward on $( - \infty , \infty )$
C)concave upward on $( - \infty , \infty )$
D)concave downward on $( - \infty , 0 )$ ; concave upward on $( 0 , \infty )$
E)concave upward on $( - \infty , 1 )$ ; concave downward on $( 1 , \infty )$

Question

Quizplus · Accepted Answer

The concavity of a function is determined by the sign of its second derivative. For $f(x) = 2x^2 + 5x - 4$, the first derivative is $f'(x) = 4x + 5$, and the second derivative is $f''(x) = 4$, which is positive for all $x$. Therefore, the graph is concave upward on $(- \infty, \infty)$.

Determine the Open Intervals on Which the Graph Of f(x)=2x2+5x−4f ( x ) = 2 x ^ { 2 } + 5 x - 4f(x)=2x2+5x−4

Determine the Open Intervals on Which the Graph Of $f ( x ) = 2 x ^ { 2 } + 5 x - 4$