# Classification of stationary points of functions?

Find and classify the stationary points of the following functions:

5x^3 - x^3 - x - 1

x^5 - x^4

(x^2) * (e^x)

I've worked them out already but just wanted to chekc my workings/answers against how others work them out...

### 1 Answer

- 10 years agoFavourite answer
1)

f(x)=5x^3 - x^3 - x - 1

f'(x)=15x^2 - 3x^2 - 1

f''(x) = 30x -6x

2)

f(x) = x^5 - x^4

f'(x) = 5x^4 - 4x^3

f''(x) = 20x^3 - 12x^2

3)

f(x) = (x^2) * (e^x)

f''(x) = (2x)(ex^(x-1))

f''(x) = 2(x+1)(ex)^x-2

So the answers would be

1)

f'(x)=15x^2 - 3x^2 - 1

f'(x) = 0 when gradient = 0 aka stationary point

15x^2-3x^2-1 = 0

12x^2 = 1

x^2 = 1/12

x = (1/12)^0.5

x = .22

2)

f'(x) = 5x^4 - 4x^3

f'(x) = 0 when gradient = 0 aka stationary point

5x^4 - 4x^3 = 0

(5)(x)(x)(x)(x) - 4(x)(x)(x) =0

Therefor x = 0, etc.

3)

f''(x) = (2x)(ex^(x-1))

f'(x) = 0 when gradient = 0 aka stationary point