Question

find h(t) if h(t) = 12.9 + 4.5t - 0.2t².
...
h(t) = \square

Explanation:

Step1: Differentiate each term

• Differentiate the constant term \(12.9\): \(\frac{d}{dt}(12.9) = 0\)
• Differentiate \(4.5t\): Using the power rule \(\frac{d}{dt}(at^n)=ant^{n - 1}\), for \(a = 4.5\) and \(n=1\), we get \(\frac{d}{dt}(4.5t)=4.5\times1\times t^{1-1}=4.5\)
• Differentiate \(-0.2t^{2}\): Using the power rule \(\frac{d}{dt}(at^n)=ant^{n - 1}\), for \(a=- 0.2\) and \(n = 2\), we get \(\frac{d}{dt}(-0.2t^{2})=-0.2\times2\times t^{2 - 1}=-0.4t\)

Step2: Combine the derivatives

\(h^{\prime}(t)=\frac{d}{dt}(12.9)+\frac{d}{dt}(4.5t)+\frac{d}{dt}(-0.2t^{2})\)
\(h^{\prime}(t)=0 + 4.5-0.4t\)

Answer:

\(h^{\prime}(t)=4.5-0.4t\)