SOLUTION: find b such that f(x)=-4x^2+bx+3 has a maximum value of 50

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Question 393700: find b such that f(x)=-4x^2+bx+3 has a maximum value of 50
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find b such that f(x)=-4x^2+bx+3 has a maximum value of 50
:
Max value occurs at the axis of symmetry, the axis of symmetry formula x =-b/(2a)
x = %28-b%29%2F%282%2A-4%29
x = %28-b%29%2F%28-8%29
x = b%2F8 is the axis of symmetry
we can also write it
b = 8x
:
-4x^2 + bx + 3 = 50
Replace b with 8x
-4x^2 + (8x)x + 3 = 50
-4x^2 + 8x^2 + 3 = 50
+4x^2 = 50 - 3
x^2 = 47%2F4
x = 3.4278
:
Find the value of b
b%2F8 = 3.4278
b = 8*3.4278
b = 27.4226
:
The equation f(x) = -4x^2 + 27.4226x + 3, has a max of 50 at x=3.4278