let f(x)= -x² + ax + b. determine the constants a and b such that f has a relative maximum at x = 3 and the…

let f(x)= -x² + ax + b. determine the constants a and b such that f has a relative maximum at x = 3 and the relative maximum value is 16. a = b = need help? read it master it

let f(x)= -x² + ax + b. determine the constants a and b such that f has a relative maximum at x = 3 and the relative maximum value is 16. a = b = need help? read it master it

Answer

Explanation:

Step1: Find the derivative of f(x)

$f'(x)=-2x + a$

Step2: Set the derivative equal to 0 at x = 3

Since there is a relative - maximum at x = 3, $f'(3)=0$. $-2\times3 + a=0$ $a = 6$

Step3: Substitute a and x into the original function

We know that $f(x)=-x^{2}+ax + b$, and when x = 3, f(3)=16, and a = 6. $f(3)=-3^{2}+6\times3 + b=16$ $-9 + 18 + b=16$ $9 + b=16$ $b=7$

Answer:

$a = 6$ $b = 7$