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Math - Exponential

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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)

  • Math - Exponential - ,

    ***Smallest value: 10e^(-144)

  • Math - Exponential - ,

    Agree with the first one

  • Math - Exponential - ,

    Agree with the second one

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