Homework Soursefxx33x27x3 on the interval 03 what value of c satisfies the
f(x)=x^3-3x^2+7x-3 on the interval [0,3]
what value of c satisfies the conclusion of the theorem
what value of c satisfies the conclusion of the theorem
Solution
f(x) = x^3 - 3x^2 + 7x - 3
f\'(x) = 3x^2 - 6x + 7
f\'(c) = (f(3) - f(0))/(3 - 0)
3c^2 - 6c + 7 = 7
3c^2 - 6c = 0
3c(c - 2) = 0
c = 0, 2
0 < c < 3 --> c = 2
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![f(x)=x^3-3x^2+7x-3 on the interval [0,3] what value of c satisfies the conclusion of the theoremSolutionf(x) = x^3 - 3x^2 + 7x - 3 f\'(x) = 3x^2 - 6x + 7 f\'(c)](/WebImages/35/fxx33x27x3-on-the-interval-03-what-value-of-c-satisfies-the-1103405-1761583485-0.webp "f(x)=x^3-3x^2+7x-3 on the interval [0,3] what value of c satisfies the conclusion of the theoremSolutionf(x) = x^3 - 3x^2 + 7x - 3 f\'(x) = 3x^2 - 6x + 7 f\'(c)")
