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f(x)=−3x2+12x−11 Step 1 of 2 : Find all values of x that correspond to horizontal tangent lines. Select "None" if the function does not have any values of x that correspond to horizontal tangent lines.

Answer :

xero099

Answer:

[tex]x = 2[/tex] corresponds to a horizontal line tangent to [tex]f(x) = -3\cdot x^{2}+12\cdot x -11[/tex].

Step-by-step explanation:

Let [tex]f(x) = -3\cdot x^{2}+12\cdot x -11[/tex], its first derivative represents a formula to determine the slope of lines tangent to a given point of the curve and slopes of horizontal tangent line corresponds to those values of [tex]x[/tex] such that [tex]f'(x) = 0[/tex].

We obtain the first derivative and equalize it to zero:

[tex]-6\cdot x +12 = 0[/tex]

And solve it for [tex]x[/tex]:

[tex]x = 2[/tex]

[tex]x = 2[/tex] corresponds to a horizontal line tangent to [tex]f(x) = -3\cdot x^{2}+12\cdot x -11[/tex].

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