Solve the problem
-The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 12 and 13 seconds?
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if the concentration increases between 12 and 13 seconds, we need to calculate the derivative $G'(x)$ and evaluate it at a point between 12 and 13 seconds (for example, at $x = 12.5$). The derivative $G'(x)$ represents the rate of change of the concentration with respect to time. If $G'(x) > 0$ for $x$ in the interval (12, 13), then the concentration is increasing in that interval.The derivative $G'(x)$ is:$$G'(x) = -0.024x^3 + 0.420x^2 - 1.06x + 1.79$$Evaluating $G'(x)$ at $x = 12.5$ (or any point between 12 and 13) will give us a positive value, indicating that the rate of change of the concentration is positive, hence the concentration is increasing between 12 and 13 seconds.

Solve the Problem -The Polynomial G(x)=−0.006x4+0.140x3−0.53x2+1.79xG ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 xG(x)=−0.006x4+0.140x3−0.53x2+1.79x

Solve the Problem
-The Polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$