Determine the real value(s) of x for which the line tangent to is horizontal.
D) x = 0

Question

Determine the real value(s) of x for which the line tangent to  is horizontal.
D) x = 0

Quizplus · Accepted Answer

The slope of the tangent line to a function f(x) at a point x=a is equal to the derivative of f(x) evaluated at x=a. 
The derivative of the given function 11eaa88b_9254_4d04_a696_ef873b760343_TB5869_11 is:
f'(x) = 4x^3 - 5x^2 - 12x
If the tangent line is horizontal, then its slope is 0. So, we need to solve the equation f'(x) = 0:
4x^3 - 5x^2 - 12x = 0
Factorizing the equation, we get:
x(4x^2 - 5x - 12) = 0
x = 0 or x = 5/4 or x = -3
The only real solution is x = -3, which corresponds to choice C: 11eaa88b_9254_9b27_a696_edaf450b09a3_TB5869_11.

Determine the Real Value(s) of X for Which the Line