Question

find f(t) if f(t)=3t^2 - 9t + 8.
f(t)=□

Explanation:

Step1: Apply power - rule to first term

The power - rule for differentiation is $\frac{d}{dt}(at^n)=nat^{n - 1}$. For the term $3t^2$, $a = 3$ and $n = 2$. So, $\frac{d}{dt}(3t^2)=3\times2t^{2 - 1}=6t$.

Step2: Apply power - rule to second term

For the term $-9t$, $a=-9$ and $n = 1$. So, $\frac{d}{dt}(-9t)=-9\times1t^{1 - 1}=-9$.

Step3: Differentiate the constant term

The derivative of a constant $C$ (in this case $C = 8$) is 0, i.e., $\frac{d}{dt}(8)=0$.

Step4: Combine the derivatives

$f'(t)=\frac{d}{dt}(3t^2)+\frac{d}{dt}(-9t)+\frac{d}{dt}(8)$. Substituting the results from the previous steps, we get $f'(t)=6t-9 + 0$.

Answer:

$6t-9$