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Chapter 7: Problem 13

Find the derivative of the function. $$ f(t)=-3 t^{2}+2 t-4 $$

Short Answer

Expert verified
The derivative of the function \(f(t) = -3t^2 + 2t - 4\) is \(f'(t) = -6t + 2\).

Step by step solution

01

Identify the Terms and Power Rule

The function given is a second-degree polynomial function, \(f(t) = -3t^2 + 2t - 4\). According to the Power Rule; the derivative of a function of the form \(t^n\) is given by \(n*t^{n-1}\). In this case, the power rule will be applied separately to each term in the function.
02

Apply the Power Rule to Each Term

Apply the power rule to each term. For the first term, \( -3t^2 \), the power rule gives us \( -3*2*t^{2-1}\), which simplifies to \( -6t \). For the second term, \( 2t \), the power rule gives us \( 2*1*t^{1-1} = 2 \). The last term \( -4 \) is a constant and its derivative is zero.
03

Combine the Derivatives

The derivatives found from each term in the function are combined to give the derivative of the entire function. This results in \(f'(t) = -6t + 2 + 0\), which simplifies to \(f'(t) = -6t + 2\).

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