Calculus Question

Question

The function f(x)=5x+7x−1 has one local minimum and one local maximum.

This function has a local maximum at x=  with value 

and a local minimum at x=  with value 

Answer 1

f'(x)=5-7x^-2

equals zero

x=+/-√(7/5)

f''(x)=14x^-3

when x>0, f''(x)>0, and critical point is a minimum

when x<0, f''(x)<0, and critical point is a maximum

Answer 2

I'm guessing there is a mistake in what you wrote. Do you perhaps mean to have a cube on the leading x? I would guess that there is a square on the leading x but then the resulting function would not have both a local max and local min.