Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the Problem seems to require calculus, use a graphical or numerical approach to estimate the Solution. A cyclist is riding on a path whose elevation is modeled by the function $f ( x ) = 0.2 x$ where $x$ and $f ( x )$ are measured in miles. Find the rate of change of elevation when $x = 5$.
$y = f ( x )$

A) calculus, 2
B) precalculus, $0.2$
C) calculus, $0.2$
D) precalculus, 2
E) precalculus, $0.45$

Question

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the Problem seems to require calculus, use a graphical or numerical approach to estimate the Solution. A cyclist is riding on a path whose elevation is modeled by the function $f ( x ) = 0.2 x$ where $x$ and $f ( x )$ are measured in miles. Find the rate of change of elevation when $x = 5$.
$y = f ( x )$

A) calculus, 2 
B) precalculus, $0.2$ 
C) calculus, $0.2$ 
D) precalculus, 2 
E) precalculus, $0.45$

Quizplus · Accepted Answer

The problem asks for the rate of change of elevation, which is simply the slope of the tangent line to the function $f(x)$ at $x=5$. Since the function is linear ($f(x)=0.2x$), its slope is constant and equal to the coefficient of $x$, which is $0.2$. Therefore, the rate of change of elevation at $x=5$ is $0.2$. This can be found using precalculus knowledge of linear functions and their slopes. No calculus is required.

Decide Whether the Following Problem Can Be Solved Using Precalculus f(x)=0.2xf ( x ) = 0.2 xf(x)=0.2x

Decide Whether the Following Problem Can Be Solved Using Precalculus $f ( x ) = 0.2 x$