Calculus

posted by .

let d2y/dx2= 6x. Find a solution to the differential equation that is continuous for negative infinity to positive infinity and whose graph passes through the point (0,1) and has a horizontal tangent there.

  • Calculus-IVP -

    Initial value problem.

    f"(x)=6x
    f'(x)=3x² + C
    f(x)=x³ + Cx + D
    (each integration introduces one integration constant: C and D)

    Given f(0)=1, and f'(0)=0
    f(0) = 1 = 0³+C(0)+D => D=1
    f'(0) = 0 = 3(0)² + C => C=0
    Therefore
    f(x)=x³+1
    Since the function is a polynomial, its domain is (-∞,∞).

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Find the horizontal asymptote of f(x)=e^x - x lim x->infinity (e^x)-x= infinity when it's going towards infinity, shouldn't it equal to negative infinity, since 0-infinity = - infinity lim x-> -infinity (e^x)-x= infinity
  2. calculus

    For what value of the constant c is the function f continuous on the interval negative infinity to positive infinity?
  3. calculus

    For what value of the constant c is the function f continuous on the interval negative infinity to positive infinity?
  4. calculus

    State which of the conditions are applicable to the graph of y = f(x). (Select all that apply.) lim x→infinity f(x) = −infinity lim x→a+ f(x) = L lim x→infinity f(x) = L f is continuous on [0, a] lim x→infinity …
  5. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) …
  6. Please check my Caclulus

    1. Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward. A. (negative infinity, infinity) B. (negative infinity, -1) U (1, infinity) C. (negative infinity, 0) U (0, infinity) D. (1, infinity) E. none of these I …
  7. Please check my Calculus

    1. Find all points of inflection of the function f(x)=x^4-6x^3 A. (0, 0) B. (0, 0), (9/2, -2187/16) C. (3, -81) D. (0, 0), 3, -81) E. none of these I got D. I found the second derivative and solved for x and plugged values into original …
  8. Please check my Calculus

    1. Find the value(s) of c guaranteed by Rolle’s Theorem for f(x)=x^2+3x on [0, 2] A. c=-3/2 B. c=0, 3 C. Rolle’s Theorem doesn’t apply as f is not continuous on [0, 2] D. Rolle’s Theorem doesn’t apply as f(0) does not equal …
  9. calculus

    hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!! A population …
  10. Calculus

    Sketch the graph of the function that has the following properties. f is continuous on (-infinity, infinity). points: (-1,2), (0, 0), (-1,0) f'(x)>0 at (-infinity, -1) f'(-1)=0 f'(x)<0 at (-1, 1) f'(1)=0 f'(x)>0 on (1, infinity) …

More Similar Questions