Find f.

f'(x) = 3x^(1/2) + 10x^(3/2)

 

f(x) = 2x^(3/2) + 4x^(5/2) + k where I is a constant

 

Since f(1) = 7 we have:  7 = 2 + 4 + k so that k = 1

 

Hence:   f(x) = 2x^(3/2) + 4x^(5/2) + 1

 

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