Question

How do you find local maximum value of f using the first and second derivative tests: `f(x) = x^5 - 5x + 5`?

Answer 1

`f(-1)=-1+5+5=9" is local maximum"`.

Explanation:

It is known from Calculus that a fun. `f : RRrarrRR` has a local

maxima at `x=c", then,":(1): f'(c)=0, &, :(2): f''(c)<0`.

`f(x)=x^5-5x+5 rArr f'(x)=5x^4-5, and, f''(x)=20x^3`.

`"Now, "f'(x)=0rArr5x^4-5=0rArrx=+-1`

Since, `f''(-1)=-20<0,`, we find that,

`f(-1)=-1+5+5=9" is local maximum"`.