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

Question

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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Lydia 2 months 2021-10-09T06:31:27+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-09T06:32:42+00:00

    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

    0
    2021-10-09T06:33:24+00:00

    Answer:

    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

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