DC3

Calculus Level 4

Consider the following equation

ln ⁡ ( f ′ ( x ) ) + 2 ln ⁡ ( f ′ ( x ) ) + 3 ln ⁡ ( f ′ ( x ) ) + . . . . + n ln ⁡ ( f ′ ( x ) ) = x \ln(f'(x)) + 2\ln(f'(x)) + 3\ln(f'(x)) +....+ n\ln(f'(x)) = x , with f ′ ( x ) f'(x) greater than 0 always

Determine f ( 1950 ) 325 \frac{f(1950)}{325} when n is 25 if f ( 325 ) f(325) is 0 for the given n


The answer is 400.710.

Natalia Dcruz by Natalia Dcruz , 21, India

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1 solution

X X
Jun 2, 2018

325 ln ⁡ ( f ′ ( x ) ) = x , f ′ ( x ) = e x 325 , f ( x ) = 325 × e x 325 + C 325\ln(f'(x))=x,f'(x)=e^{\frac x{325}},f(x)=325\times e^{\frac x{325}}+C ,so f ( 1950 ) − f ( 325 ) 325 = e 6 − e \frac{f(1950)-f(325)}{325}=e^6-e

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