Question
Q1)
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Q2)
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Q3)
Suppose y = 9(x - 4) + 24 is the tangent line to f(x) at x = 4. Find the value of each of the following quantities. f(4+h) - f(4) / h = f(4) = A function T(x) is continuous and differentiable with values given in the table below. Use the values in the table to estimate each of the following. Use best estimates and round your answer to two decimal places. The average rate of change of T(x) between x = 44 and 71 is approximately The rate if change of T(x) at x = 53 is approximately T(44 + h) - T(44) / h Suppose g(x) is increasing and curve and concave up everywhere and g(A) = 3, g'(A) = 15, h = 0. 01 Estimate each of the following: g(A - h) g(A + h) Are the estimates in part (a) larger or smaller than the true function values? Why? Larger because g(x) is concave up. Smaller because g(x) is concave up. Larger because g(x) is increasing. Smaller because g(x) is increasing.
Explanation / Answer
1)
9
f(4) = 24
2)
(a)4/36 = 1/9 = 0.12
(b)
rate of change = -10/18 = -5/9 = -0.56
3)
g(A-h) = 2.85
g(A+h) =3.15
(b)
option B
