KSizzle1998 KSizzle1998

08-02-2021
Mathematics

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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=

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LammettHash LammettHash

09-02-2021

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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