Question

exercises 3.1 defining the derivative
score: 4/27 answered: 2/12
question 3
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if $f(x)=25x + 22$, find $f(-6)$.
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Explanation:

Step1: Recall derivative formula

For a linear - function \(y = ax + b\), its derivative \(y^\prime=a\). Given \(f(x)=25x + 22\), using the power - rule \((x^n)^\prime=nx^{n - 1}\), where for \(y = 25x+22\), the derivative \(f^\prime(x)\) of \(f(x)\) is: \(f^\prime(x)=\frac{d}{dx}(25x + 22)=\frac{d}{dx}(25x)+\frac{d}{dx}(22)\). Since \(\frac{d}{dx}(25x)=25\) and \(\frac{d}{dx}(22) = 0\), then \(f^\prime(x)=25\).

Step2: Evaluate \(f^\prime(-6)\)

Since \(f^\prime(x)\) is a constant function (its value does not depend on \(x\)), when \(x=-6\), \(f^\prime(-6)=25\).

Answer:

25