3. a) Suppose a function y = g(x) satisfies g(0) = 0 and 0 g'(x)...

 

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3. a) Suppose a function y = g(x) satisfies g(0) = 0 and 0 ≤ g'(x) ≤ 1 for all values of x in the interval 0≤x≤3. Explain carefully why the graph of 9 must lie entirely in the triangular region shaded below: y₁ 3 2 2 3 = b) Suppose you learn that g(1) = .5 and g(2) 1. Draw the smallest shaded region in which you can guarantee that the graph of g must lie. 4. Suppose h is differentiable over the interval 0≤x≤ 3. Suppose h(0) = 0, and that 5≤h'(x) ≤1 for 0≤x≤1 0 ≤h'(x) ≤.5 for 1≤x≤2 -1≤h'(x) ≤0 for 2 ≤x≤3 Draw the smallest shaded region in the x, y-plane in which you can guarantee that the graph of y=h(x) must lie. 3. a) Suppose a function y = g(x) satisfies g(0) = 0 and 0 ≤ g'(x) ≤ 1 for all values of x in the interval 0≤x≤3. Explain carefully why the graph of 9 must lie entirely in the triangular region shaded below: y₁ 3 2 2 3 = b) Suppose you learn that g(1) = .5 and g(2) 1. Draw the smallest shaded region in which you can guarantee that the graph of g must lie. 4. Suppose h is differentiable over the interval 0≤x≤ 3. Suppose h(0) = 0, and that 5≤h'(x) ≤1 for 0≤x≤1 0 ≤h'(x) ≤.5 for 1≤x≤2 -1≤h'(x) ≤0 for 2 ≤x≤3 Draw the smallest shaded region in the x, y-plane in which you can guarantee that the graph of y=h(x) must lie.

Answer rating: 100% (QA)

h is differentiable over interval 0x3 and h0 0 Given 05hx 1 for 0x1 0hx 05 for 1x2 1hx 0 for 2x3 Fro... View the full answer