let (f(x)=-2x(x - 1)). then (f(0)=) and after simplifying (f(x)=) hint: you may want to expand and simplify…
let (f(x)=-2x(x - 1)). then (f(0)=) and after simplifying (f(x)=) hint: you may want to expand and simplify the expression for (f(x)) first.
Answer
Explanation:
Step1: Expand f(x)
[ \begin{align*} f(x)&=-2x(x - 1)\ &=-2x^2+2x \end{align*} ]
Step2: Differentiate f(x) using power - rule
The power - rule states that if (y = ax^n), then (y^\prime=anx^{n - 1}). For (y=-2x^2+2x), (f^\prime(x)=-2\times2x^{2 - 1}+2\times1x^{1 - 1}=-4x + 2)
Step3: Find f'(0)
Substitute (x = 0) into (f^\prime(x)): (f^\prime(0)=-4\times0+2=2)
Answer:
(f^\prime(0)=2) (f^\prime(x)=-4x + 2)