Question

f(x) = {2x + 5 for x <= - 1; -x^2+6 for x >= - 1. if f is the function defined above, then f(-1) is a -2 b 2 c 3 d 5 e nonexistent

Explanation:

Step1: Determine the relevant function part

Since $x = - 1$ and for $x\leq - 1$, $f(x)=2x + 5$.

Step2: Differentiate the function

The derivative of $y = 2x+5$ using the power - rule $\frac{d}{dx}(ax + b)=a$ (where $a = 2$ and $b = 5$) is $f'(x)=2$.

Step3: Evaluate the derivative at $x=-1$

Since $f'(x)=2$ for all $x$ in the domain $x\leq - 1$, then $f'(-1)=2$.

Answer:

B. 2