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Mean value theorem

Jarrod Asuncion Period 1 Brose. Mean value theorem. Equation. f(b) – f(a) = f’(c) b – a Slope = f’(c) . Sample Problem. Find the number c satisfying the Mean Value Theorem for f(x)= sinx on the interval [1,1.5], correct to three decimal places. . Step 1: .

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Mean value theorem

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  1. Jarrod Asuncion Period 1 Brose Mean value theorem

  2. Equation f(b) – f(a) = f’(c) b – a Slope = f’(c)

  3. Sample Problem Find the number c satisfying the Mean Value Theorem for f(x)=sinx on the interval [1,1.5], correct to three decimal places.

  4. Step 1: Use formula [1,1.5] is the same as [a,b]. The function is f(x) = sinx. f(1.5) – f(1) = 0.997 – 0.841 = 0.312 = f’(c) 1.5 – 1 0.5

  5. Step 2: Take derivative of function and set it equal to f’(c) and substitute ‘x’ for ‘c’. And solve for ‘c’. f(x)=sinx =› f’(x)=cosx f’(x)=f’(c) & substitute ‘x’ for c. trying to find ‘c’ cosc=0.312 c=1.253

  6. IMPORTANT The value for ‘c’ must be between the interval given. c=1.253 Interval [1,1.5] C satisfies the Mean Value Theorem (MVT)

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