elementary calc

posted by .

f(x) passes through (0,2). the slope of f at any point is 3 times the y-coordinate. find the derivative at 1

  • elementary calc -

    When a derivative of a function is a multiple of the y value of the function, it suggests an exponential function.

    let the function be y = a e^(kx), where a and k are constanst

    dy/dx = ak e^(kx)

    given ak e^(kx) = 3y = 3(a e^(kx))
    then ak = 3a
    k = 3
    so we know y = a e^(3x)
    at (0,2)
    2 = a e^(0)
    a = 2

    then y = 2 e^(3x)
    then dy/dx = 6 e^(3x)
    when x=1
    dy/dx = 6 e^3

  • elementary calc -

    dy/dx = 3 y

    dy/y = 3 dx

    ln y = 3 x + c

    y = C e^3x

    if x = 0, y = 2
    y = 2 e^3x

    when x = 1
    y = 2 e^3 = 40

    dy/dx = 3y = 120

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc

    Find a parabola with the equation y=ax^2+bx+c and has slope 4 at x=1, slope -8 at x=-1, and passes through the point (2,15). Thanks
  2. Math/Algebra do u know how to do slope intercept?

    The following problems are in slope,point slope, and slope intercept forms of a line. Could you check these thanks. Find the slope intercept form of a line that passes through these two points (-4,4) and (2,1) Answer: y= -1/2x-2 Find …
  3. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation …
  4. calculus

    The graph of f(x) passes through the point (0,3) . The slope of f at any point P is 3 times the y- coordinate of P . Find f(1)
  5. calculus

    the graph of f(x) passes through the point (0,6). the slope of f at any point P is 2 times the y-coordinate of P. find f(1)
  6. Calculus Help Please!!! Check

    A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = …
  7. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  8. calculus

    8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has …
  9. Math please.

    What is the y-intercept of y = 2/3x + 2? I have to write it out but how?
  10. Calculus

    Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point

More Similar Questions