Let f ( x ) {\displaystyle f(x)} be a function differentiable at x = 1 {\displaystyle x=1} and let g ( x ) = f ( x ) x 2 {\displaystyle g(x)={\frac {f(x)}{x^{2}}}} . The line tangent to the curve y = f ( x ) {\displaystyle y=f(x)} at x = 1 {\displaystyle x=1} has slope 3 {\displaystyle 3} while the line tangent to the curve y = g ( x ) {\displaystyle y=g(x)} at x = 1 {\displaystyle x=1} has slope 4 {\displaystyle 4} . What is f ( 1 ) {\displaystyle f(1)} ?
