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H asked in Science & MathematicsMathematics · 2 months ago

Let f be a function with f(2)=4 and derivative f'(x)=√ (x^3 +1 ) Using a tangent line approximation to graph of f at x=2 estimate f(2.2)?

2 Answers

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  • Find f'(2)

    f'(2) = sqrt(2^3 + 1) = sqrt(9) = 3

    You need a line with a slope of 3 that passes through (2 , 4)

    y - 4 = 3 * (x - 2)

    Now find the value of y when x = 2.2

    y - 4 = 3 * (2.2 - 2)

    y - 4 = 3 * 0.2

    y = 4 + 0.6

    y = 4.6

    That's all there is to it.

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  • Dylan
    Lv 6
    2 months ago

    f(2.2) ≈ f(2) + 0.2*f'(2)

     ≈ 4 + 0.2*√((2)^3+1)

     ≈ 4.6

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