SOLUTION: Find the particular antiderivative that satisfies the following conditions: f''(x) = 12 x^3

SOLUTION: Find the particular antiderivative that satisfies the following conditions: f''(x) = 12 x^3 - 2; \quad f(0) = 4, \quad f'(0) = -2

Question 945874: Find the particular antiderivative that satisfies the following conditions:
f''(x) = 12 x^3 - 2; \quad f(0) = 4, \quad f'(0) = -2

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the particular antiderivative that satisfies the following conditions:
f''(x) = 12 x^3 - 2; \quad f(0) = 4, \quad f'(0) = -2
------
f'(x) = 3x^4 - 2x + C
quad f'(0) = -2 --> C = -2 (not sure what the "quad" means)
---
f'(x) = 3x^4 - 2x - 2
---
f(x) =
f(0) = 4 --> C = 4
f(x) =
RELATED QUESTIONS
Find a function f that satisfies the conditions. f ''(x) = x2, f '(0) = 4, f(0) = (answered by user_dude2008)

Write an equation that satisfies the given conditions:... (answered by stanbon,Edwin McCravy,robertb)

Find an equation of a rational function f that satisfies the conditions: vertical... (answered by stanbon)

Find a cubic polynomial function f(x) that satisfies both of the following conditions: (answered by htmentor)

Suppose that f(x) and g(x) are functions which satisfy f(g(x)) = x^2 \quad \text{and}... (answered by CPhill)

Given f(x) = 2x^2 - 3x + 4, find the following: f(4) f(-3)... (answered by tutorcecilia)

Is my antiderivative correct? Q: Find the function f such that f'(x) = 2sin(x) +... (answered by jim_thompson5910)

If a linear function f satisfies the conditions : f ( -3 ) = - 2 and f ( 3 ) = 16 , find... (answered by user_dude2008,ewatrrr)

Sketch a graph of a function f that satisfies the following conditions: f does NOT... (answered by robertb)