# Math - Exponential

posted by
**Anonymous**
.

Please check if my answers are correct! Thank you.

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)