Question Solved1 Answer For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (c) f(x)=(x-1)¹0 over [0.2] For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (c) f(x)=(x-1)¹0 over [0.2] For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (d) y=e¹ over [0,1] Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] •f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] • f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a
TFZURK The Asker · Calculus
Transcribed Image Text: For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (c) f(x)=(x-1)¹0 over [0.2] For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (d) y=e¹ over [0,1] Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] •f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] • f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a
More Transcribed Image Text: For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (c) f(x)=(x-1)¹0 over [0.2] For the following exercises, (a) determine whether the Mean Value Theorem applies for the functions over interval[a, b]. (b) Find values of c guaranteed by the Mean Value Theorem. (d) y=e¹ over [0,1] Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] •f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a Theorem 3.5: Mean Value Theorem Let f be a function. If • fis continuous over the closed interval [a, b] • f differentiable (a, b). Then, there exists at least one point c e(a, b) such that f'(c)=f(b)-f(a) b-a
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Since f(x)=(x-1)^(10) is polynomial function, and we know that polynomal function is continuwus and differentiahle on R.:.f(x)=(x-1)^(10) is continuous on [0,2] and differentiable on (0,2)By Mean Value Theirem EE c in(a,b) s.t{:[f^(')(c)=(f(b)-f(a)quad b-a)/(b-a)","b=2],[f^(')(x)=10(x-1)^(49)quad{(dx^(n))/(dx)=nx^(n-1)}],[10(x-1)^(9)=(f(2)-f(0))/(2-0)],[10(c-1)^(9)=(1-1)/(2)=0],[10(c-1)^(9)=0 ... See the full answer