calculas
posted by jenny .
The function f(x)= (8x7)e^2x has one critical number. Find it

calculas 
MathMate
A critical point in the domain of x is a value of x at which the function is not differentiable or where the derivative is zero.
See: http://en.wikipedia.org/wiki/Critical_point_%28mathematics%29
For the case in point:
f(x)= (8x7)e^2x
f'(x) can be found using the product rule and the chain rule as
f'(x):=2(8x3)*e^(2x)
Setting f'(x)=0 and solving for x, we get e^2x=0 or x=3/8.
Since the range of e^2x excludes 0, it is a solution to be rejected. So the unique point required is x=3/8.
Respond to this Question
Similar Questions

high school calculas
Find the (a) the local extrema, (b) the intervals on which the function is increasing, (c) the interval on which the function is decreasing h(x)=2/x 
Math
The critical numbers of the function: f(t)=7t^(2/3)+t^(5/3) f'(t)=14/3t^(1/3)+(5/3)t^(2/3) I got 0 as a critical number but it is hard for me to factor the f'(t). Whats the other critical number? 
Calculus (pleas help!)
Consider the function f(x)=12x^5+60x^4−100x^3+4. For this function there are four important intervals: (−INF,A], [A,B] ,[B,C] , and [C,INF) where A, B, and C are the critical numbers. Find A, B, and C. At each critical … 
Math
Find any critical numbers of the function. (Enter your answers as a commaseparated list.) g(x) = x^7 − 7x^5 Honestly, I have no idea how to find the critical number! 
Calculas
Find any critical numbers of the function. (Enter your answers as a commaseparated list.) g(t) = t sqrt6 − t , t < 13/3 I don't even know how to start out! 
calculus
I've done the first question but I cannot get any farther. I'm so stuck. Please explain or just help me to figure out the next steps. A printed poster is to have a total area of 837 square inches with top and bottom margins of 7 inches … 
Calc 3
If a function of one variable is continuous on an interval and has only one critical number, then a local maximum has to be an absolute maximum. But this is not true for functions of two variables. Show that the function f(x,y)= 3xe^y … 
Calculus
The function f(x) = (9 x+2)e^{6 x} has one critical number. Please help me find the critical number! 
Calculas
The slope of the tangent line to the graph of a function, h(t) is 7/2t The function passes through the point (5,3) Find h(4) 
calculus
The function f(x) = (7 x+9)e^{2 x} has one critical number. Find it.