calculus
posted by mabel .
find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)

dy/dx = 3xy
dy/y = 3x dx
ln y = 3x^2/2+c
y = Ce^3x^2/2
2 = Ce^0
C = 2
y = 2e^(3x^2/2)
y' = 2e^(3x^2/2)*(3x)
= 3xy
Respond to this Question
Similar Questions

cal
Equations of the tangent lines to hyperbola xy=1 that pass through point (1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (1,1)? 
Math calculus
Given f(x) = x ^ 3  x ^ 2 4x +4 Find the zeros of f. Write an equation of the line tangent to the graph of f at x = 1 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0,8) … 
math
i have more than one question so if u no any of the answers please tell me 1.) write the pointslope form of the equation of the line with slope 2 passing through the point ( 5, 9). 2.) write the pointslope form of an equation … 
Calculus
1. Given the function f defined by f(x) = x^3x^24X+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) … 
calculus antiderivation
Given that the graph of f(x) passes through the point (2,5) and that the slope of its tangent line at (x, f(x))is 3x+5, what is f(3) ? 
Calculus
Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) … 
Math
Find the function f, given that the slope of the tangent line at any point (x,f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=6(2x7)^5 at (4, 3/2) 
calculus
1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? 
Calculus AB
Could someone please help me with these tangent line problems?