Final answer:
To find the value of f(-1), substitute -1 into the function. To find the value of f(1), substitute 1 into the function. To find all values of c in the interval (-1, 1) such that f'(c) = 0, take the derivative of the function and set it equal to 0. The only value of c in the interval (-1, 1) such that f'(c) = 0 is c = 0.
Step-by-step explanation:
To find the value of f(-1), we substitute -1 into the function f(x) = 1 - x^(2/3). f(-1) = 1 - (-1)^(2/3) = 1 - (-1)^(2/3) = 2.
To find the value of f(1), we substitute 1 into the function f(x) = 1 - x^(2/3). f(1) = 1 - (1)^(2/3) = 1 - (1) = 0.
To find all values of c in the interval (-1, 1) such that f'(c) = 0, we take the derivative of the function f(x) and set it equal to 0. The derivative of f(x) is f'(x) = -2/3 * x^(-1/3). Setting this equal to 0, we have -2/3 * x^(-1/3) = 0. Solving for x, we find that x = 0. Therefore, the only value of c in the interval (-1, 1) such that f'(c) = 0 is c = 0.
The Question is incomplete. The complete question is
Consider the following function.
f(x) = 1 - x^(2/3)
Find (-1) and f(1). Find all values c in (-1, 1) such that f'(c)=0