Question

question for the following equation, evaluate f(1). f(x)=3x^3 - 5x^2 + 3x

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule $(x^n)'=nx^{n - 1}$, if $f(x)=3x^{3}-5x^{2}+3x$, then $f'(x)=3\times3x^{2}-5\times2x + 3=9x^{2}-10x + 3$.

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

Substitute $x = 1$ into $f'(x)$. So $f'(1)=9\times1^{2}-10\times1 + 3$.
$f'(1)=9 - 10+3=2$.

Answer:

2