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Question

# Indicate whether the statement is true or false. If $R(w)=w^{3}$ then R'(-2) is negative.

Solution

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Let's check the statement:

\begin{align*} R'(w)&=\frac{d}{dw}[w^3] && \text{Differentiate.}\\ &\color{#c34632}=3w^2 && \text{Apply the \textbf{Power Rule}.}\\ \\ R'(-2)&=3\cdot (-2)^2 && \text{Substitute w=-2.}\\ &\color{#c34632}=12 && \text{Simplify.}\\ \end{align*}

Also, if we look at the graph, we can see that at $w=-2$, the slope of a tangent line is $\textbf{positive}$. So the statement is false.

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