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Find a quadratic polynomial verifying f(-3) = – 18, f'(-3) = 16, f''(-3) = - 6.

Find A Quadratic Polynomial Verifying F3 18 F3 16 F3 6 class=

Sagot :

LammettHash

Let f(x) = ax ² + bx + c. Then

f '(x) = 2ax + b

f ''(x) = 2a

f (-3) = -18, so

9a - 3b + c = -18

f ' (-3) = 16, so

-6a + b = 16

f '' (-3) = -6, so

2a = -6

Then a = -3, b = -2, and c = 3, so that

f(x) = -3x ² - 2x + 3

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