dj asked in Science & MathematicsMathematics · 2 months ago

 Suppose that 4≤𝑓′(𝑥)≤6 for all values of 𝑥. Use the Mean Value Theorem to find values for the inequality below.?

a≤𝑓(2)−𝑓(−2)≤b

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  • 1 month ago

    According to mean value theorem,

    min f '(x) ≤ (f(x1) - f(x2))/(x1-x2) ≤ max f '(x)

    min f '(x) = 4

    max f '(x) = 6

    Let x1=2 and x2=-2

    4 ≤ (f(2) - f(-2))/(2+2) ≤ 6

    4 ≤ (f(2) - f(-2))/4 ≤ 6

    multiply by 4

    16 ≤ f(2) - f(-2) ≤ 24

    a=16

    b=24

  • 1 month ago

    straight line with slope 4,

    and straight line with slope 6.

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