Which of the following properties are true of the graph of y = 10 $\mathrm { e } ^ { 2 x }$ ?
(I) It is concave up.
(II) The y-intercept is (0, 2).
(III) It has a minimum at x = 0.
(IV) y is positive for x ≥ 0 and negative for x

Question

Which of the following properties are true of the graph of y = 10 $\mathrm { e } ^ { 2 x }$ ? 
(I) It is concave up.
(II) The y-intercept is (0, 2).
(III) It has a minimum at x = 0.
(IV) y is positive for x ≥ 0 and negative for x < 0.
A) I only
B) I and III
C) I and II
D) III and IV

Quizplus · Accepted Answer

The graph of $y = 10e^{2x}$ is concave up because the second derivative is positive for all x. The y-intercept is $10e^{0} = 10$, not (0, 2). There is no minimum, as the function increases exponentially for all x. Finally, $y$ is positive for all x, not just for $x \geq 0$, because $e^{2x}$ is always positive.

Which of the Following Properties Are True of the Graph e2x\mathrm { e } ^ { 2 x }e2x

Which of the Following Properties Are True of the Graph $\mathrm { e } ^ { 2 x }$