if f(x)=6x² - 4x + 9, find f(1).\nf(1)= (simplify your answer.)

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$, for $f(x)=6x^{2}-4x + 9$, we have $f'(x)=\frac{d}{dx}(6x^{2})-\frac{d}{dx}(4x)+\frac{d}{dx}(9)$. So $f'(x)=2\times6x-4+0 = 12x - 4$.

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

Substitute $x = 1$ into $f'(x)$. Then $f'(1)=12\times1-4$. $f'(1)=12 - 4=8$.

Answer:

8