## Question

# Calculate the average rate of change of the given function f over the intervals [a, a + h] where h=1, 0.1, 0.01, 0.001, and

Calculate the average rate of change of the given function f over the intervals [a, a + h] where h=1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h=0.01, 0.001, and 0.0001.) (Round your answers to five decimal places.) h=1 h = 0.1 h= 0.01 h = 0.001 h = 0.0001 4 f(x): =;a = 4 x Use a quick approximation to estimate the derivative of the given function at the indicated point. HINT [See Example 2(a).] (Round your answer to three decimal places.) f'(2)= f(x) = x + 2 x=2 Compute f'(x) algebraically for the given value of a. HINT [See Examples 1 and 3.] a=1 f(x) = ;a= x = f'(a) = Find the derivative of the function. HINT [See Examples 1 and 2.] h'(x) h(x) =- 1 505

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