Question

if $f(x)=2 + 7x-2x^{2}$, find $f(1)$.

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule, if \(y = ax^n\), then \(y'=nax^{n - 1}\). For \(f(x)=2 + 7x-2x^{2}\), \(f'(x)=\frac{d}{dx}(2)+\frac{d}{dx}(7x)-\frac{d}{dx}(2x^{2})\). Since \(\frac{d}{dx}(c)=0\) (where \(c\) is a constant), \(\frac{d}{dx}(7x)=7\), and \(\frac{d}{dx}(2x^{2}) = 4x\), so \(f'(x)=0 + 7-4x=7 - 4x\).

Step2: Evaluate f'(x) at x = 1

Substitute \(x = 1\) into \(f'(x)\). \(f'(1)=7-4\times1\).

Answer:

3