Calculus
posted by Rudy .
1. For the function f(x)=4x^330x^2+4:
a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema
2. For the function f(x)=(x1)^(8/11)
a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema

f' = 12x^2  60x = 12x(x5)
as you know
extrema where f'=0
increasing where f' > 0
Respond to this Question
Similar Questions

Calculus
Find the intervals on which y=1/(x^2+1)^2 is increasing and decreasing. find the first derivative which is 4x/(x^2+1)^3 you should know that if the first derivative is positive, then the function is increasing and if it is negative, … 
Basic CalculusRelative Extrema
Hello, please help me :) A question asked that I find all relative extrema of a function f(x)= x + 1/x. I'm a bit confused with my solution, but I'll show my work first..: I found f'(x) to get the critical numbers: f'(x)=1x^2 f'(x)=(x^2 … 
Calculus
Find the critical numbers of f, find the open intervals on which the function is increasing or decreasing and use the first derivative test to identify all relative extremes f(x) = 3 + cos^2 x 0<x<2pie 
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 … 
Calculus
Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined. Find A Find B For each of the following … 
Calculus
find the intervals on which f(x) is increasing and decreasing along with the local extrema. f(x)=x^4 + 18x^2 I took the derivative and got: f'(x)= 4x^3 + 36x When I set this to zero, I get the imaginary number 3i. I can't get test … 
Please check my Calculus
1. Find all points of inflection: f(x)=1/12x^42x^2+15 A. (2, 0) B. (2, 0), (2, 0) C. (0, 15) D. (2, 25/3), (2, 25/3) E. none of these I got D. I found the second derivative and equaled it to 0 and solved for x. I plugged the x values … 
Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4x)x^3 for x>0. A. Find the xcoordinate of the critical point of f. Determine whether the point is a relative … 
Brief Calculus
Increasing and Decreasing Functions. Let f(x) = 4x^3  9x^2 30x +6 A. Find all critical numbers of f(x) B. Give the open intervals where f (x) is increasing and decreasing and clearly label each.