How Do You Find a Function Whose Integral is x^3 and Has a Tangent Line x+y=0?

In summary, the conversation is discussing finding the equation f(x) whose integral is \int x^{3} and has a tangent x+y=0. The solution involves using the knowledge that f(x) = 1/4x^4+c due to the given integral, and finding the point where the derivative of f(x) is equal to the slope of the given tangent line. However, there is confusion over the specific details and equations involved in solving the problem.
  • #1
flyers
29
0

Homework Statement



Find the equation f(x) who's integral is [tex]\int x^{3}[/tex] and has a tangent x+y=0

Homework Equations


The Attempt at a Solution



I know that f(x) is 1/4x4+c because of the integral. The tangent is the derivative of f(x) at some point

i have the equations

y=x3+c
y=-x

but solving these equations gives me two unknowns...
 
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  • #2
Well, at what point does x^3 equal negative 1 (the slope of y=-x)
 
  • #3
What you have written is not very clear. From what I can tell, f(x) = (1/4)x4 + C.

You're given that f is tangent to the graph y = -x. This means that f'(x) = x3 has to equal -1 (the slope of the line y = -x). It also means that the graph of f has to have a point in common with the line y = -x.
 
  • #4
-1?
so

1/4x4+c=1
1/4(-1)+c=1
c=3/4

f(x)= 1/4x4+3/4
 
  • #5
flyers said:
-1?
-1 for what?
flyers said:
so
Why 1? You're not explaining what you're doing, which makes it extremely difficult to understand your work.
flyers said:
1/4x4+c=1
1/4(-1)+c=1
c=3/4

f(x)= 1/4x4+3/4
 
  • #6
Sorry, I was replying to Char. limit's question
 
  • #7
Can you post the problem exactly as it is worded? I'm having a hard time believing this is what you have actually been given:
flyers said:
Find the equation f(x) who's integral is [itex]\int x^{3}[/itex]
and has a tangent x+y=0

especially the part that says "who's integral is [itex]\int x^{3}[/itex]..."
 

FAQ: How Do You Find a Function Whose Integral is x^3 and Has a Tangent Line x+y=0?

What is a function?

A function is a mathematical relationship between two quantities, where for every input there is exactly one output.

What is the definition of tangent?

The tangent of a point on a curve is a straight line that just touches the curve at that point, and has the same slope as the curve at that point.

How is the tangent of a function calculated?

The tangent of a function can be calculated using the derivative of the function at a given point. This derivative represents the slope of the tangent line at that point.

Why is the tangent important in calculus?

The tangent is important in calculus because it allows us to find the instantaneous rate of change of a function at a specific point. This is crucial in many real-world applications, such as determining velocity or acceleration.

Can a function have more than one tangent at a given point?

No, a function can only have one tangent at a given point. This is because the tangent represents the slope of the function at that point, and a function can only have one slope at a given point.

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