Answer the following questions about $F(x) = -x^2 + 35x + 348$. (A) Calculate the change in $F(x)$ from $x = 10$ to $x = 15$.
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The change in $F(x)$ is given by $\Delta F = F(15) - F(10)$. First, we need to calculate $F(10)$. Substitute $x = 10$ into the function: $F(10) = -(10)^2 + 35(10) + 348$ $F(10) = -100 + 350 + 348$ $F(10) = 250 + 348$ $F(10) = 598$ Show more…
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(A) Calculate the change in $F(x)$ from $x=10$ to $x=15$. (B) Graph $F^{\prime}(x)$ and use geometric formulas (see Appendix $C$ ) to calculate the area between the graph of $F^{\prime}(x)$ and the $x$ axis from $x=10$ to $x=15 .$ (C) Verify that your answers to (A) and (B) are equal, as is guaranteed by the fundamental theorem of calculus. $$ F(x)=9 x+120 $$
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