A relation between a function f(x) and its derivative f'(x) = x√f(x) is given with an initial condition on f(x) as f(4)=16. One needs to find the value of the second derivative of the function i.e., f"(4). Also an expression to f(x) in terms of x is to be evaluated.
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First the value of the second derivative is calculated using the product rule and the initial condition. Then using the variables separable Method of solving the differential equations, we solve the equation and find the expression for ...
Derivatives are investigated. The solution is detailed and well presented.