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 of $G(x)$ and evaluate it at a point between 12 and 13 seconds, say at $x = 12.5$. The derivative $G'(x)$ represents the rate of change of the concentration with respect to time. If $G'(x) > 0$ at $x = 12.5$, it means the concentration is increasing between 12 and 13 seconds.The derivative $G'(x) = -0.024x^3 + 0.420x^2 - 1.06x + 1.79$.Evaluating $G'(12.5)$ gives a positive value, indicating that the concentration is indeed increasing between 12 and 13 seconds.

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