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The derivative of a function f(x) is given by f'(x)=3x^2-6x+4. The tangent line at the point (2,9) is parallel to another tangent line at the point ( a,b) . Find a .

Respuesta :

Answer:2

Step-by-step explanation:

Given

The derivative of a function is [tex]f'(x)=3x^2-6x+4[/tex]

The slope at (2,9) is

[tex]\Rightarrow 3(2)^2-6\times 2+4=4[/tex]

the tangent at (2,9) is parallel to another tangent at (a,b) i.e. their slopes are equal

[tex]\Rightarrow 4=3a^2-6a+4\\\Rightarrow 3a^2-6a=0\\\Rightarrow\ 3a(a-2)=0\\\Rightarrow a=0\ \text{or}\ a=2[/tex]

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