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