Find all x-values for which the slope of the tangent is 0 for the given function.

Question

Find all x-values for which the slope of the tangent is 0 for the given function. ​  ​

Quizplus · Accepted Answer

To find the x-values for which the slope of the tangent is 0, we need to find the critical points of the function, i.e., the points where the derivative of the function is zero or undefined.

The derivative of the given function is,

f'(x) = 3x^2 - 6x - 27

Setting f'(x) = 0, we get

3x^2 - 6x - 27 = 0

Dividing both sides by 3, we get

x^2 - 2x - 9 = 0

Using the quadratic formula, we get

x = (2 ± sqrt(4 + 36))/2

x = 1 ± 2sqrt(2)

Therefore, the critical points of the function are x = 1 + 2sqrt(2) and x = 1 - 2sqrt(2).

At these points, the slope of the tangent is 0. The correct choice is therefore B, which gives the value x = 1 - 2sqrt(2).

Find All X-Values for Which the Slope of the Tangent