Word Problem Help: Slope of Tangent Line, Finding a Zero

[quiteso]

Here's the problem - I'm desperate!

Inch the Worm was crawling down the curve f(x)= x^3 + 3x^2 - 4x - 5 one day. When Inch reached a height of 3 units above the x-axis, he decided to go off on a tangent. After crawling down the tangent for a while, he bumped into the x-axis. Find the exact position (no decimal approximations) of Inch on the x-axis.

 

[wjm11]

Inch the Worm was crawling down the curve f(x)= x^3 + 3x^2 - 4x - 5 one day. When Inch reached a height of 3 units above the x-axis, he decided to go off on a tangent. After crawling down the tangent for a while, he bumped into the x-axis. Find the exact position (no decimal approximations) of Inch on the x-axis.

Set the function equal to 3 and solve. You will get three solutions (x values).

Find the derivative of the function.

Plug in the x values you found above into the derivative to get three slopes.

Use the three slopes and the three points (where f(x) = 3) to define three lines.

Find the intersection of these lines with the x-axis.

 

[BigGlenntheHeavy]

\(\displaystyle Here \ is \ its \ graph. \ You \ didn't \ specify \ if \ the \ bug \ came \ down \ from \ infinity \ or \ a \ relative \ max.\)

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