Question

find the F (the anti-derivative?) of f''(x)=3/(x)^(1/2), where at f'(4)=7 and F(4)=20

Answer 1

yay integration! finally something interesting..

Answer 2

we cant integrate yet, my calc instructor wont allow it. He wants us to find the anti derivatives

Answer 3

f"(x) = 3/x^(1/2) = 3*x^(-1/2), integrate this.

Answer 4

Integral is anti derivative..

Answer 5

Integral of (3x^(-1/2)) = 3x^((-1/2)+1)/((-1/2)+1)

Answer 6

f'(x) = 3x^(1/2)/(1/2) = 6x^(1/2) + C

Answer 7

f'(4)=7 =>
6*sqrt(4) + C = 7
6*2 + C = 7
12+c = 7, c = 5

Answer 8

f'(x) = 6x^(1/2) + 5

Answer 9

repeat the process:
integrate (f'(x)) => get _________ + C
plug in F(4) = 20 and get the original F

Answer 10

thank you.