Question

hw8 defining the derivative (targets l6, d3; §3.1)
score: 2/5 answered: 3/5
question 4
if (f(x)=6 + 3x-4x^{2}), find (f(-1)).
question help: video message instructor

Explanation:

Step1: Find the derivative of f(x)

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, for $f(x)=6 + 3x-4x^{2}$, we have $f'(x)=\frac{d}{dx}(6)+\frac{d}{dx}(3x)-\frac{d}{dx}(4x^{2})$. Since $\frac{d}{dx}(c)=0$ (where $c$ is a constant), $\frac{d}{dx}(3x)=3$ and $\frac{d}{dx}(4x^{2}) = 8x$. So $f'(x)=0 + 3-8x=3 - 8x$.

Step2: Evaluate f'(-1)

Substitute $x=-1$ into $f'(x)$. We get $f'(-1)=3-8\times(-1)$.
$f'(-1)=3 + 8=11$.

Answer:

11