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

[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?

 

[Mystic998]

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.

 

[sutupidmath]

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 the 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.
$$\frac{e^x(cosx + sinx)}{cos^2(x)}=0$$

 

[sutupidmath]

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

 

[rocomath]

The only thing wrong with your derivative is your sign.

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

 

[HallsofIvy]

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