Calculus
posted by Elizabeth .
Find the critical numbers of y=x(4x)^1/2.
The answer is x=8/3 but I got x=7/2.

y = x√(4x)
y' = 1√(4x) + x * 1/2 * 1/√(4x) * 1
= √(4x)  x/(2√(4x))
= (2(4x)  x)/(2√(4x))
= (83x)/(2√(4x))
assuming x≠4, we just have to find where the numerator is zero.
x = 8/3
Respond to this Question
Similar Questions

Calculus
How do you find the critical numbers and the end points of this function: f(x)=2x^33x^212x+5 i calculated the critical numbers as x=1 and x=2 is this right? 
Calculus  another question
"Find the absolute minimum value of the function f(x) = x ln(x)". I know that one of the critical values is 1 (domain restriction). Am I right? 
Calculus
Find the critical numbers of the function g(t)=5t7 If you find g'(t) you just get 5 so would there be no critical numbers? 
calculus
Consider a differentiable functionf having domain all positive real numbers, and for which it is known that f'(x)=(4x)^3 for x.0 a. find the xcoordinate of the critical point f. DEtermine whether the point is a relative maximum … 
math
If y= (x^2+20)/(x4) Find all critical Numbers. After get f' i got the answer 5/4. What did i do wrong or is that the critical number? 
Calculus
If y= (x^2+20)/(x4) Find all critical Numbers. After get f' i got the answer 5/4. What did i do wrong or is that the critical number? 
calculus
Please help!! *f(x)= x(x+6)^1/2 find two x intercepts. Then show that f'(x)=0 at some point between the 2 x intercepts. *Use mean value theorem for f(x)= x(x^23x+1) for interval [1,4] I FOUND DERIAVITIVE WHICH IS 3X^26X+1.THEN? 
help please!
f(x)=x+1/x Find all critical numbers. Find where the function is increasing and decreasing. Find critical points and identify each as a relative maximum, relative minimum, or neither. Find second order critical numbers and tell where … 
Please check my Calculus
1. Find all critical values for f(x)=(9x^2)^⅗ A. 0 B. 3 C. 3,3 D. 3, 0, 3 E. none of these I got D. I found the derivative and solved for critical numbers. 2. Find all intervals on which the graph of f(x)=(x1)/(x+3) is concave … 
critical numbers
How would I find the critical numbers of f'(x)=(x3)^3(x+4)(x^2+1)?