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    Find the derivative f 'of f and tangent line

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    Let f(x) = x2 + 4x.
    (a) Find the derivative f 'of f.
    (b) Find the point on the graph of f where the tangent line to the curve is horizontal.
    Hint: Find the value of x for which f '(x) = 0.
    (c) Sketch the graph of f and the tangent line to the curve at the point found in part (b).

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.
    f(x)=7x-3x^2 at (-1,-10)

    Use the Intermediate Value Theorem to find the value of c such that f(c) = M. f(x)=x^2-x+1 on [1,8]; M=43.

    The final question is in the attachment with a graph attached to it.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:15 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/derivative-tangent-line-456914

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.)

    (Select all that apply.)

    The function f is discontinuous at x=0 because f is not defined at x=0

    The function f is discontinuous at x=0 because f (x) does not exist.

    The function f is discontinuous at x=0 because f (x) exists, but this limit is not equal to f (0).

    The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of (x).

    --------------------------------------------------------------------------------
    ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬

    Use the Intermediate Value Theorem to find the value of c such that f(c) = M.

    c = 7

    ¬¬¬¬¬¬¬¬¬-------------------------------------------------------------
    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.

    m = 13
    y = 13x+3

    Let f(x) = x2 + 4x.

    f(x) = x2 + 4x (a) Find the derivative f 'of f.
    f '(x) = 2x+4

    (b) Find the point on the graph of f where the tangent line to the curve is horizontal.
    Hint: Find the value of x for which f '(x) = 0.

    (x, y) = (-2,-4)

    (c) Sketch the graph of f and the tangent line to the curve at the point found in part (b).

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:15 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/derivative-tangent-line-456914

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