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Need work shown, please a) Suppose a function f is continuous on the interval [a,b]. If...

Need work shown, please

a) Suppose a function f is continuous on the interval [a,b]. If f(a) is negative and f(b) is positive, explain why there must be a number c between a and b such that f(c) = 0.

(Context: related to “Intermediate Value Theorem”.)

b) Use the idea from part (a) to show that the equation x^5 = 2 − 2x has a solution in the interval [0, 1].

(Hint: A solution for an equation f(x) = g(x) is equivalent to a solution for the equation f (x) − g(x) = 0.)

Math   Calculus   
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