# Calculus

Find a function f such that f '(x) = 3x3 and the line 3x + y = 0 is tangent to the graph of f.
f(x) =

1. 👍
2. 👎
3. 👁
1. dy/dx = 3 x^3
then
y = (3/4) x^4 + c

slope of line y = -3x + 0 = -3
so where does our slope = -3?
3 x^3 = -3
x = 1
so make y the same for the function and the line at x = 1
line at x = 1 is y = -3
so
(3/4)x^4 + c = -3 at x = 1
3/4 + c = -3 = -12/4
c = -15/4
so
f(x) = (3/4) x^4 -15/4
or
4 y = 3 x^4 - 15

1. 👍
2. 👎

## Similar Questions

1. ### Math (Secant Lines)

Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? -Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5. -Find the slope of each secant line -Use the results

2. ### pre calc

f(x)=-3x+2 a) express the slope of the secant line of each function in terms of x and h. b) find msecant for h=.5, .1, and.01 at x=1. c) find the equation for the secant line at x=1 with h=1.01 I got -3 for a but don't know how to

3. ### calc

let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative of f is given by f'(x)= (1 - Ln(x))/x squared. a) write equation for the line tangent to the graph of f at x=e squared b) Find the x-coordinate of the critical

4. ### Math (Calculus) (mean value theorem emergency)

Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c

1. ### Calculus

The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 +

2. ### Maths

x2-x-6 is a factor of f(x)=3x3+px2+qx+6. Find the values of the constants p and q and state the zeros of f(x).

3. ### calculus

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (64, 8), we know that (64, 8) is a point on the line. So we just

4. ### Calculus

Find k such that the line is tangent to the graph of the function. Function: f(x)=kã(x) Line: y=x+4

1. ### Math- Calculus

Find an equation of the line that is tangent to the graph of f and parallel to the given line Function: f(x) = x^3 Line 3x-y+1 = 0 ._.; I know the derivative of the function is 3x^2 and I do have the answer in the back of my book

2. ### Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of

3. ### calculus

5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the

4. ### calculus

Find y'' by implicit differentiation. 3x3 + 4y3 = 1