Given-a-rational-function-f-x-ax-2-bx-c-x-q-has-minimum-point-at-2-9-and-maximum-point-at-2-1-Find-value-of-a-b-c-and-q-

Question Number 156188 by naka3546 last updated on 09/Oct/21

G i v e n a r a t i o n a l f u n c t i o n

f (x) = \frac{{a x}^{2} + b x + c}{x + q}

h a s m i n i m u m p o i n t a t (- 2, 9) a n d m a x i m u m p o i n t a t (2, 1) .

F i n d v a l u e o f a, b, c, a n d q .

Commented by MJS_new last updated on 09/Oct/21

we have 4 unknowns and need 4 equations

(1) f (- 2) = 9

(2) f (2) = 1

(3) f^{'} (- 2) = 0

(4) f^{'} (2) = 0

solve this to get

a = - 1

b = 5

c = - 4

q = 0

Commented by naka3546 last updated on 09/Oct/21

T h a n k y o u, s i r .