if f(x)=2x² - 5x + 3, find f(3).\n\nf(3)= (simplify your answer.)

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$, for $f(x)=2x^{2}-5x + 3$, we have $f'(x)=\frac{d}{dx}(2x^{2})-\frac{d}{dx}(5x)+\frac{d}{dx}(3)$. So $f'(x)=2\times2x-5+0 = 4x-5$.

Step2: Evaluate f'(x) at x = 3

Substitute $x = 3$ into $f'(x)$. So $f'(3)=4\times3-5$.

Step3: Calculate the result

$f'(3)=12 - 5=7$.

Answer:

7