solve this problem algebraically, using your knowledge of derivatives. do not solve by graphing. what is the…
solve this problem algebraically, using your knowledge of derivatives. do not solve by graphing. what is the absolute maximum of the function f(x)= -4x² - 8x + 20 on the domain -2,1? no absolute maximum on the given domain. 15 24 8
Answer
Explanation:
Step1: Find the derivative
The derivative of $f(x)=-4x^{2}-8x + 20$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=-8x-8$.
Step2: Find the critical points
Set $f'(x) = 0$. So, $-8x-8 = 0$. Solving for $x$ gives $-8x=8$, then $x=-1$.
Step3: Evaluate the function at critical and end - points
Evaluate $f(x)$ at $x=-2,x=-1,x = 1$. For $x=-2$: $f(-2)=-4(-2)^{2}-8(-2)+20=-4\times4 + 16+20=-16 + 16+20=20$. For $x=-1$: $f(-1)=-4(-1)^{2}-8(-1)+20=-4 + 8+20=24$. For $x = 1$: $f(1)=-4(1)^{2}-8(1)+20=-4-8 + 20=8$.
Answer:
24