Posted by Jacob on Wednesday, February 27, 2013 at 7:08pm.
Let f(x) = −x2 + ax + b.
Determine the constants a and b such that f has a relative maximum at x = 2 and the relative maximum value is 13.

Applied Calculus  Steve, Thursday, February 28, 2013 at 12:23am
f'(x) = 2x+a
if f'=0 at x=2, then a=4
f(x) = x^2 + 4x + b
f(2) = 13 = 4+8+b
b=5
f(x) = x^2 + 4x + 5 = (x+1)(x5)
vertex is at x=(51)/2 = 2 as desired

Applied Calculus  Angela, Wednesday, October 12, 2016 at 10:56pm
Correction: b=9
f(x)=x^2 +4x+b
if f(2)=13=2^2+4(2)+b
then f(2)=13=4+8+b
17=8+b
9=b
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