Concept explainers
Another look at the Fundamental Theorem
71. Use Exercise 69 to prove that if two trails start at the same place and finish at the same place, then regardless of the ups and downs of the trails, they have the same net change in elevation.
69. Suppose that f and g have continuous derivatives on an interval [a, b]. Prove that if f(a) = g(a) and f(b) = g(b), then
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- Determine whether each of the following statements is true or false and explain why. The derivative of a function exists whenever the function is continuous.arrow_forwardDetermine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.arrow_forwardDetermine whether each of the following statements is true or false, and explain why. The derivative of a product is the product of the derivatives.arrow_forward
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