Question

I am not able to find maxima of this function

Answer 1

\[\huge f(x)=x ^{5}-5x ^{4}+5x ^{3}-10\]

Answer 2

I got the first derivative as:-
\[x ^{2}-4x+3\]
So by setting them equal to zero i get
x=1 or x=3

Now if i do the 2nd derivative test i get
x = 2 which is MINIMA :(

Answer 3

The first derivative goes like this: 5x^4 - 20x^3 .....

Answer 4

yeah factor it out and set it equal to zero

Answer 5

f'(x) = 5x^4 - 20x^3 + 15x^2 = 0
5x^2(x^2 - 4x + 3) = 0
5x^2(x-3)(x-1) = 0

Critical Points are: x = 0, 1 and 3.

Answer 6

won't you move 5x^2 to the right?

Answer 7

No. You equate the first derivative to zero and solve for x.

Answer 8

What are all the values of x that will make the first derivative equal zero?
x = 0, 1 and 3.

Answer 9

So, ok after this what we should do

Answer 10

Take the second derivative and test each critical point.

Answer 11

so 1 is a maxima point thanks

Answer 12

Correct.