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4 February, 07:47

Let f (x) equals x squared minus 10 x plus 6. a. Find the values of x for which the slope of the curve yequals f (x) is 0. b. Find the values of x for which the slope of the curve yequals f (x) is negative 6.

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Answers (2)
  1. 4 February, 10:45
    0
    a) x = 5

    b) x = 2

    Step-by-step explanation:

    The given function is f (x) = x² - 10x + 6 and we want to find the values of x such that slope of the curve equals to 0 and - 6. This can be done by taking the derivative of the function f (x) and setting that equal to 0 and - 6 respectively.

    When slope of curve = 0

    Take the derivative of the function f (x)

    f (x) = x² - 10x + 6

    f' (x) = 2x - 10 + 0

    f' (x) = 2x - 10

    Now put f' (x) = 0

    0 = 2x - 10

    2x = 10

    x = 10/2 = 5

    Hence x = 5

    When slope of curve = - 6

    We have already taken the derivative so we just have to put f' (x) = - 6

    -6 = 2x - 10

    2x = - 6 + 10

    2x = 4

    x = 4/2 = 2

    Hence x = 2
  2. 4 February, 11:43
    0
    The question is:

    Let f (x) = x² - 10x + 6

    a. Find the values of x for which the slope of the curve y = f (x) is 0.

    b. Find the values of x for which the slope of the curve y = f (x) is - 6.

    Answer:

    (a) The value of x for which the slope is 0 is 5

    (b) The value of x for which the slope is - 6 is 2

    Step-by-step explanation:

    Given y = f (x) = x² - 10x + 6

    The Slope is given as dy/dx = f' (x)

    It is obtained by differentiating y = f (x) once with respect to x.

    Let us find the first derivative of

    y = x² - 10x + 6

    That is

    dy/dx = 2x - 10

    Now

    (a) We want to find the value of x for which the slope dy/dx = 0

    We set

    2x - 10 = 0

    And solve for x, to have

    2x = 10

    x = 10/2 = 5

    (b) The value of x for which the slope is - 6

    We set

    2x - 10 = - 6

    2x = - 6 + 10 = 4

    x = 4/2 = 2
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