`f'(x) = 1 + 3sqrt(x), f(4) = 25` Find `f`.

Textbook Question

Chapter 4, 4.9 - Problem 31 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`f'(x)=1+3sqrt(x)`

`f(x)=int(1+3sqrt(x))dx`

`f(x)=x+3(x^(1/2+1)/(1/2+1))+c`

`f(x)=x+3(x^(3/2)/(3/2))+c`

`f(x)=x+3(2/3)x^(3/2)+c`

`f(x)=x+2x^(3/2)+c`

Now let's find constant c , given f(4)=25

`f(4)=25=4+2(4)^(3/2)+c`

`25=4+2(2^2)^(3/2)+c`

`25=4+2(2^3)+c`

`25=4+16+c`

`c=25-20=5`

`:.f(x)=x+2x^(3/2)+5`

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