For the function, find the points on the graph at which the tangent line is hori

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)

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