Thread: FTC w/ Chain Rule and Concavity
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Old January 2nd, 2009, 04:08 PM
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skeeter skeeter is offline
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f(x) = \int_0^x 15t^2 - 2t^3 + 24 \, dt

f'(x) = 15x^2 - 2x^3 + 24

f''(x) = 30x - 6x^2

if f(x) is concave up on (a,b), then f''(x) > 0 on (a,b)

30x - 6x^2 > 0

6x(5 - x) > 0

f''(x) > 0 on (0,5) ... b-a = 5
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