For the function, find the points on the graph at which the tangent line is hori
ID: 2890111 • Letter: F
Question
For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. f(x)- 6x2 -4x+4 Select the correct choice below and, if necessary, fill in the answer box within your choice. 3 The point(s) at which the tangent line is horizontal is (are) Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) The tangent line is horizontal at all points of the graph. O B. There are no points on the graph where the tangent line is horizontal. C.Explanation / Answer
f(x) = 6x^2 - 4x + 4
differentiate with respect to x,
f’(x) = d/dx (6x^2 - 4x + 4)
= 12x - 4
for tangent to be horizontal, f’(x) =0
so,
12x - 4 = 0
x = 4/12 = 1/3
f(1/3) = 6(1/3)^2 - 4(1/3) + 4
= 6/9 - 4/3 + 4
= 2/3 - 4/3 + 4
= (2-4+12)/3
= 10/3
Answer should be A (1/3,10/3)