Determine the value(s) of x, if there are any, for which the slope of the tangent line to does not exist.
D) The slope exists for all values of x.

Question

Determine the value(s) of x, if there are any, for which the slope of the tangent line to  does not exist.
D) The slope exists for all values of x.

Quizplus · Accepted Answer

The slope of the tangent line to a function does not exist at points where the function has a vertical tangent, which occurs at points where the derivative is undefined or infinite. 
Taking the derivative of 11eaa88b_9254_e949_a696_bf45d22b37cb_TB5869_11, we get:
11eaa88b_9255_5e7d_a696_3377fba3a1c1_TB5869_11' = 2x + 1
Setting the derivative equal to undefined or infinite, we have:
2x + 1 = undefined or infinity
This occurs only when x is -1/2. Thus, the answer is C, since only the points 11eaa88b_9255_5e7d_a696_3377fba3a1c1_TB5869_11 and 11eaa88b_9255_858e_a696_cb966c2457b8_TB5869_11 have a vertical tangent.

Determine the Value(s) of X, If There Are Any, for Which