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)(x-5)

vertex is at x=(5-1)/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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