Question

question 3 · 1 point
find slope of the line tangent to the graph of f(x)=-x² + 5x - 1 at x = 0.
provide your answer below:
slope = □

Explanation:

Step1: Recall the derivative formula

The derivative of a function $y = f(x)$ gives the slope of the tangent line. For $f(x)=-x^{2}+5x - 1$, use the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$.
The derivative $f^\prime(x)=\frac{d}{dx}(-x^{2}+5x - 1)=-2x + 5$.

Step2: Evaluate the derivative at the given point

We want to find the slope of the tangent line at $x = 0$. Substitute $x = 0$ into $f^\prime(x)$.
$f^\prime(0)=-2(0)+5$.

Answer:

$5$