4. -/1 points details my notes tanapcalc10 4.4.018.mi. find the absolute maximum value and the absolute…

4. -/1 points details my notes tanapcalc10 4.4.018.mi. find the absolute maximum value and the absolute minimum value, if any, of the function. (if an answer does not exist, enter dne.) f(x)=-x² + 10x + 4 on 7, 10 maximum minimum need help? read it master it

4. -/1 points details my notes tanapcalc10 4.4.018.mi. find the absolute maximum value and the absolute minimum value, if any, of the function. (if an answer does not exist, enter dne.) f(x)=-x² + 10x + 4 on 7, 10 maximum minimum need help? read it master it

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(x)=-x^{2}+10x + 4$ is $f^\prime(x)=-2x + 10$.

Step2: Find critical - points

Set $f^\prime(x)=0$, so $-2x + 10 = 0$. Solving for $x$ gives $x = 5$. But $x = 5$ is not in the interval $[7,10]$.

Step3: Evaluate the function at endpoints

Evaluate $f(x)$ at $x = 7$ and $x = 10$. When $x = 7$, $f(7)=-7^{2}+10\times7 + 4=-49 + 70+4=25$. When $x = 10$, $f(10)=-10^{2}+10\times10 + 4=-100 + 100+4=4$.

Answer:

maximum: 25 minimum: 4