Question

How do you find an equation for the function f'(x)=πsecπxtanπx whose graph passes through the point (1/3,1)?

Answer 1

Assuming that y is a polynomial, since you only have three conditions, it must be a quadratic (since the second derivative is a constant). So

y=A+Bx+Cx2

y′′=2C implies C=12. Now, compute A and B in order the function goes through the two points.