Graphing e^x = x^2: Tips for Accurate Drawings

In summary, the conversation discusses the graph of e^x = x^2 and how it may be initially drawn incorrectly. The speaker mentions using a plotting tool to accurately plot the graph and also mentions the concept of derivatives for determining steepness.
  • #1
phospho
251
0
The graph e^x = x^2:

I originally drew it like this:

ov3Zx.png


But it's actually:

Q68TS.png


If I come across more complex graphs in the future, is there a way to know which one is steeper than the other, to draw it accurately ?
 
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  • #2
phospho said:
The graph e^x = x^2:

I originally drew it like this:

ov3Zx.png


But it's actually:

Q68TS.png


If I come across more complex graphs in the future, is there a way to know which one is steeper than the other, to draw it accurately ?

You could plot some actual points of interest to see where the plots are...
 
  • #3
A good plotting tool exists at fooplot.com -- by the way, "The graph e^x = x^2:" makes little sense.
 
  • #4
phospho said:
If I come across more complex graphs in the future, is there a way to know which one is steeper than the other, to draw it accurately ?

Yes, they're called derivatives, but you study those in calculus and since you posted this in precalculus I'll leave it at that.
 

FAQ: Graphing e^x = x^2: Tips for Accurate Drawings

What is the significance of graphing e^x = x^2?

The equation e^x = x^2 represents the intersection of two important mathematical functions: the exponential function (e^x) and the quadratic function (x^2). Graphing this equation can help us understand the relationship between these two functions and how they behave at their intersection.

What are some tips for accurately graphing e^x = x^2?

One tip is to plot several points on both the exponential and quadratic functions and then find their intersection. Another tip is to use a graphing calculator or software to graph the equation, which can provide a more precise drawing.

What are the key features of the graph of e^x = x^2?

The key features of this graph include a single point of intersection, where the exponential function crosses the quadratic function. The graph also shows that the exponential function grows at a faster rate than the quadratic function as x increases.

How does the value of e affect the graph of e^x = x^2?

The value of e, also known as Euler's number, is approximately 2.71828. It determines the steepness of the exponential function and can affect the position of the point of intersection with the quadratic function. As the value of e increases, the graph of e^x will become steeper and the point of intersection will shift to the right.

What are some real-life applications of graphing e^x = x^2?

The equation e^x = x^2 has applications in many fields, including physics, biology, and finance. For example, it can be used to model population growth and compound interest. In physics, it can represent the relationship between velocity and acceleration. In biology, it can describe the growth of bacteria or the spread of a disease. It can also be used in optimization problems in economics and engineering.

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