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Differentiate f(t) = √(36 ln(t) + 5t)
f'(t) = (1/2) * (36 ln(t) + 5t)^-1/2 * (36/t + 5)
f'(t) = (1/2)* (36/t + 5)/((36 ln(t) + 5t)^1/2
f'(t) = (36 + 5t) / (2t √(36lnt + 5t))
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Find the largest & smallest values of:
F(x) 10e^(g(x)), g(x) = x² - 24x for 0 ≤ x ≤ 13
g'(x) = 2x - 24
0 = 2x - 24
x = 12
g(12) = -144
g(0) = 0
g(13) = -143
Largest value: 10
Smallest value: e^(-144)
Differentiate f(t) = √(36 ln(t) + 5t)
f'(t) = (1/2) * (36 ln(t) + 5t)^-1/2 * (36/t + 5)
f'(t) = (1/2)* (36/t + 5)/((36 ln(t) + 5t)^1/2
f'(t) = (36 + 5t) / (2t √(36lnt + 5t))
-----
Find the largest & smallest values of:
F(x) 10e^(g(x)), g(x) = x² - 24x for 0 ≤ x ≤ 13
g'(x) = 2x - 24
0 = 2x - 24
x = 12
g(12) = -144
g(0) = 0
g(13) = -143
Largest value: 10
Smallest value: e^(-144)
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