Consider the function f ( x ) whose second derivative is f ' ' ( x )= 10x + 9sin( x ). If f ( 0 ) = 4 and f ' ( 0 ) = 2 , what is f ( 3 )?

Answer 1

f"(x) = 10x + 9sinx

f'(x) = 5x^2 -9cosx + c

f'(0) = 2 = -9cos(0) + c = -9 +c

c =2+9 = 11

f'(x) =5x^2 -9cosx +11

f(x) = (5/3)x^3 -9sinx + 11x + k

f(0) = 4 = + k

k=4

f(x) = (5/3)x^3 - 9sinx + 11x +4

f(3) = (5/3)(3)^3 -9sin3 +11(3) +4

= 45 +33+4 - 0.471 (if 3 means 3 degrees and not 3 radians)

=81.529

IF 3 means 3 radians then pi radians = 180 and 1 radian = 180/3.14159 = 57.3 degrees

and 3 radians = 171.9 degrees, sin 171.9 = sin8.1 = 0.14, 9sin171.9 = 9sin8.1 = 1.27

f(3) = 82-1.27 = 80.73

either way f(3) = about 81