# Tutor profile: Abhishek P.

## Questions

### Subject: Calculus

how man maxima and minima does the function f(x) = (x^2 - 4)^2 has?(x is real number)

differentiating f(x) w.r.t to x and equating to zero gives the stationary points df(x)/dx = 2(x^2-4)*2x=0 thus, x=0, x=2, x=-2 are stationary points double differentiate f(x) and put the stationary points as the value of x f''(x) = 4[x(2x) + (x^2 - 4)] = 12*x^2 - 16 f''(0) = -16 < 0 (hence maximum at x = 0) f''(2) = 31>0 (hence minima at x = 2) f''(-2) = 32>0 (hence minima at x = -2) So there are two minima and one maxima

### Subject: Chemical Engineering

Is there any relationship between activation energy and chemical potential or fugacity?

Like there is gravitational potential or electrostatic potential there is chemical potential. It is basically change in the internal energy of the system by addition of a new particle at constant volume and entropy. In terms of free energy, its the change in Gibbs free energy of a system by addition of a particle at constant temperature and pressure. So basically it tells you about the reactivity of a component in a phase. Transfer of molecule will always occur from high potential to low potential.Fugacity is escapability that is tendency of a particle to prefer one phase over other. The particle will be present in the phase having low fugacity (where the escapability is least). In terms of chemical potential it is the measure of how much the chemical potential of a component in a phase differs from the chemical potential in standard state, due to change in Pressure or mol fr of component. Fugacity is analogous to partial pressure when applying thermodynamics to any non ideal system for any component. For pure ideal gases fugacity --> partial pressure.

### Subject: C Programming

Print a number 100 times without using recursion and loop

This can be done using #define directive. // Program to print "1" 100 times. // This prints 1 only once #define a cout<<"1"<<endl; // print 'a' 10 times #define b a a a a a a a a a a // print 'b' 10 times #define c b b b b b b b b b b int main() { c; return 0; }

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