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Sagot :
Explanation
We are given the function
[tex]f(x)=6x^2-4x[/tex]for part A
we are to find the derivative of the line tangent to the graph of f at x = 2
So, we will have
[tex]f^{\prime}(x)=12x-4[/tex]when x =2,
[tex]f^{\prime}(x)=12(2)-4=24-4=20[/tex]Thus, the slope at x is 20
For part B
To get the equation of the line tangent to the graph at x =2, we will substitute x =2 into f(x)
[tex]f(2)=6(2)^2-4(2)=6\times4-8=24-8=16[/tex]Thus, using the formula
[tex]\begin{gathered} y=mx+c \\ where \\ y=16,\text{ m=20,x=2} \\ 16=20\times2+c \\ 16=40+c \\ c=16-40 \\ c=-24 \end{gathered}[/tex]Therefore, the equation is
[tex]y=20x-24[/tex]Thus, the tangent line is: y= 20x -24
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