bolton8l

2022-10-08

Derivative Instantaneous rate of change

Question:

The cumulative ticket sales for the 10 days preceding a popular concert is given by

$S(x)=4{x}^{2}+50x+5000\phantom{\rule{2em}{0ex}}1\le x\le 10.$

Find the instantaneous rate of change in S(x) when x=3.

Question:

The cumulative ticket sales for the 10 days preceding a popular concert is given by

$S(x)=4{x}^{2}+50x+5000\phantom{\rule{2em}{0ex}}1\le x\le 10.$

Find the instantaneous rate of change in S(x) when x=3.

Bestvinajw

Beginner2022-10-09Added 15 answers

The instantaneous rate of change of $S(x)=4{x}^{2}+50x+5000$ w.r.t. x is given as

$\frac{dS}{dx}=\frac{d}{dx}(4{x}^{2}+50x+5000)=8x+50$

Now, substitute x=3 to find $\frac{dS}{dx}$

$\frac{dS}{dx}=\frac{d}{dx}(4{x}^{2}+50x+5000)=8x+50$

Now, substitute x=3 to find $\frac{dS}{dx}$

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