Question

Find the critical points of the function.
F(x) = x^4/5(x - 7)^2
x = (smallest value)
x =
x = (largest value)

Answer 1

do you know how to dervive any rational function?

Answer 2

um no sorry

Answer 3

okay this is the formula (without proof):
\[(\frac{ f(x) }{ g(x) })\prime =\frac{ f(x)\prime *g(x)-g(x)\prime*f(x) }{ g(x)^2 }\]

Answer 4

ok :)

Answer 5

he means differentiate, not derive.

Answer 6

or "derive the derivative"

Answer 7

now you can use the formula to see the values that makes the derivative
f(x) prime=0 , and you get this by equalizing the nuemerator with 0
for other functions, of course, the value of x when f(x) prime is undefined is a critical point , but usually in rational function that value is not in the domain of the function

Answer 8

I am sorry @zzr0ck3r I thought they are the same, aren't they? :\

Answer 9

no, common mistake.
we derive the derivative, we derive the integral, we derive the answer to the question.

but deriving alone really does not mean anything unless we had more context.

say we have a physical thing happening and we can model it with a rational equation of some sort, then we would be deriving the rational equation when we come up with said equation.

Answer 10

I think I got you @zzr0ck3r , thank you for this information :)

Answer 11

np:)

Answer 12

thanks guys i got it :)

Answer 13

you are welcome @RosieS12 :)