F(x) be polynomial function such the f(3) , f'(3) = 0 and f"(3) = -3. What is the pint (3,3)?

Answer 1

y'' = f''(3) = -3

y' = -3x + c

f'(3) = 0

0 = -3(3) + c

0 = -9 + c

c = 9

so y' = -3x + 9

integrating again:

y = (-3/2)x^2 + 9x + c

f(3) = 3 :

3 = (-3/2)(3^2) + 9(3) + c

3 = (-3/2) (9) + 27 + c

3 = -27/2 + 54/2 + c

3 = 27/2 + c

6 = 27 + 2c

-21 = 2c

c = -21/2

the polynomial is y = (-3/2)x^2 + 9x - 21/2