Question

Please helpppp i just want to know if i sm doing it right

Answer 1

9514 1404 393

Answer:

b) -9.8t +18

Explanation:

b) The instantaneous rate of change is the derivative of the height function. The power rule is separately applied to each term, and the results added.

power rule: d/dx(x^n) = nx^(n-1)

Then the derivative is ...

dh/dt = 2(-4.9t^1) +18(1 ·t^0)

dh/dt = -9.8t +18

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If you haven't been introduced to derivatives as such, then you find the instantaneous rate of change by finding the average rate of change over a vanishing interval.

`(dh)/(dt)=\displaystyle\lim\limits_(h\to 0){ (h(t+h)-h(t))/(h)}\\\\(dh)/(dt)=\lim\limits_(h\to 0)((-4.9(t+h)^2+18(t+h)+23)-(-4.9t^2+18t+23))/(h)\\\\(dh)/(dt)=\lim\limits_(h\to 0)(-4.9(2th+h^2)+18h)/(h)=\lim\limits_(h\to 0){(-9.8t +18 -4.9h)}\\\\ \boxed{(dh)/(dt)=-9.8t +18}`