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College Math

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I have been struggling with this problem I cannot get the right answer. Please give me the steps to solve this problem.
Let f(x)= (2x-9)(x^2 + 6)
(A) Find the equation of the line tangent to the graph of f(x) at x=3
(B) Find the values(s) of x where the tangent line is horizontal.

  • College Math - ,

    I would expand the function first, then find the derivative.
    f(x) = 2x^3 + 12x - 9x^2 - 54
    f '(x) = 6x^2 + 12 - 18x
    when x = 3
    f(3) = -3(15) = -45
    f '(3) = 6(9) + 12 - 18(3) = 12

    A) so you have a slope of 12 and a point (3,-45)
    Use y = mx + b to find the tangent equation

    B) set 6x^2 - 18x + 12 = 0
    and solve
    Hint: divide both sides by 6, then it factors

  • College Math - ,

    Identify the variable, constant, and coefficient of the expression: –10k + 15

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