Determine the input that produces the largest or smallest output (whichever is appropriate). State whether the output is largest or smallest. s = - 24t² + 147t + 15 A) $t = \frac { 49 } { 16 }$ ; largest B) $t = \frac { 16 } { 49 }$ ; largest C) $x = 49$ ; smallest D) $x = 49$ ; largest E) $t = \frac { 49 } { 16 }$ ; smallest

Question

Quizplus · Accepted Answer

To find the input that produces the largest or smallest output, we need to find the value of t that maximizes or minimizes the expression. We can do this by finding the derivative of the expression with respect to t and setting it equal to zero:
s' = -24S1U1P1 + 147 = 0
Solving for t, we get:
t = 49/16
To confirm that this gives a maximum, we can take the second derivative of s with respect to t:
s'' = 48S1U1P1 > 0
Since the second derivative is positive, the function has a minimum at t = 49/16. Therefore, the input that produces the largest output is t = 49/16.

Determine the Input That Produces the Largest or Smallest Output t=4916t = \frac { 49 } { 16 }t=1649​

Determine the Input That Produces the Largest or Smallest Output $t = \frac { 49 } { 16 }$