Point on a Curve: Finding the Tangent Line with Zero Slope

• Flappy
In summary, the conversation is about finding a point on the curve of the function f(x) = \frac{e^x}{cos(x)} where the slope of the tangent line to the curve has zero slope. The attempt at a solution involves finding the derivative of the function and setting it equal to zero, but there is some confusion about the correct expression for the derivative. It is recommended to wait for further clarification on the issue.
Flappy

Homework Statement

Find the point, restricting $$x\in$$(-pi/2, 0), along the curve

f(x) = $$\frac{e^x}{cos(x)}$$

where the slope of the tangent line to f has zero slope.

The Attempt at a Solution

I found the derivative of f(x) and got:

$$\frac{e^x(cosx - sinx)}{cos^2(x)}$$

Where would I go from here to find the point though?

How does the derivative relate to the slope of a tangent line to the curve?

Edit: Incidentally, the expression you've given as the derivative is incorrect.

Last edited:
well remember that the slope of the tangent line at a point in a curve is merely the derivative of that function at that point. so since you found teh derivative of the function f(x) that means that you have found the slope of that function at any point. But y ou are interested only when that slope is zero . so just equal your rezult to zero and solve for x, if you can.
$$\frac{e^x(cosx + sinx)}{cos^2(x)}=0$$

Last edited:
this looks to me like it does not have an explicit solution though!

$$f'(x)=\frac{e^x(\cos x+\sin x)}{\cos^{2}x}$$

Last edited:
Perhaps it would be better to wait for Flappy to get back to us now.

1. What is a point on a curve?

A point on a curve refers to a specific location on a graph or chart where the plotted line intersects with the axes. It is represented by a set of coordinates, typically in the form (x,y).

2. How do you find a point on a curve?

To find a point on a curve, you can either look at the graph and estimate the coordinates, or use the equation of the curve to calculate the coordinates. Simply plug in a value for x and solve for y.

3. What is the significance of a point on a curve?

Points on a curve are important because they can help us understand the relationship between the variables being plotted. They can also be used to make predictions or draw conclusions about the data.

4. Can a point on a curve have negative coordinates?

Yes, a point on a curve can have negative coordinates. This simply means that the point is located to the left or below the axes on the graph. It is important to pay attention to the signs of the coordinates when interpreting the data.

5. How does a point on a curve differ from a point on a line?

A point on a curve is different from a point on a line because a line represents a linear relationship between two variables, while a curve can represent a nonlinear relationship. Additionally, a point on a line has a constant rate of change, whereas a point on a curve may have a changing rate of change.

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