# Math

posted by .

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x)=x^(4/5)(x − 6)^2

• Math -

by the product rule ....

f ' (x) = x^(4/5) (2)(x-6) + (4/5)x^(-1/5) (x-6)^2
= (-1/5)x^(-1/5) (x-6) [10x + 4(x-6) ]
= (-2/5)x^(-1/5) (x-6) (7x-12)

= 0 for critical numbers (max,min)

-1/5x^(-1/5) = 0 ---> no solution
x-6 = 0 ---> x = 6
7x-12=0 ---> x = 12/7

take it from there

## Similar Questions

1. ### Calculus

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(p) = (p − 2)/(p^2 + 9)
2. ### help ?

Let f(x) = (x − 3)^−2.Find all values of c in (1, 4) such that f(4) − f(1) = f'(c)(4 − 1).(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
3. ### calculus

Let f(x) = (x − 3)−2. Find all values of c in (2, 5) such that f(5) − f(2) = f'(c)(5 − 2). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C=?
4. ### pre-calculas

Find the slant asymptote, if any, of the rational function. Do not graph the function. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) f(x) = x2 − 2x + 15 _____________ x + …
5. ### calculus

Determine the value(s) of x where the function will have an instantaneous rate of change of 14. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x3 + 33 x2 + 14 x + 39
6. ### Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t^(3/4) − 3t^(1/4)
7. ### Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) F(x) = x^4/5(x − 1)^2
8. ### Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^(5)e^(-6x)
9. ### Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 4 cos θ + 2 sin^2 θ
10. ### Calculus 1

Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum …

More Similar Questions

Post a New Question