Find all values of c such that f'(c) does not exist

Question

Find all values of c such that f'(c) does not exist

Using the function f(x)= (x+7)^2/5

Find all values of c such that f'(c) does not exist

c=?

Answer 1

f(x) = (x+7)^2/5

f'(x) = (2/5)(x+7)^–3/5 = 2/[5(x+7)^3/5]

The only value of c where f'(c) does not exist is

c = –7 (because the zero denominator makes f'(7) undefined)

Note

But f'(c) does exist for all other values of c.

(x+7)^3/5 = [(x+7)^1/5]³ and (x+7)^1/5 is not like a square root. (x+7)^1/5 is still a real number when x + 7 < 0

Answer 2

f(x) = (x+7)^2/5

f'(x) = (2/5)(x+7)^-3/5 = 2 / [5 ⁵√(x + 7)³]

f'(x) is defined for all x ≠ -7.

Answer 3

f'(x) does not exist for all c such that

c ≤ -7