Calculus
posted by Anna .
let f(x)=x*e^x For what value of x is the slope of the line tangent to the graph of function f at [x,f(x)] equal to 1/2?

f(x)=xe^x,
f'(x)=e^x+xe^x=(x+1)e^x
For the tangent to have a slope of 1/2, equate
f'(x)=1/2 and solve for x:
(x+1)e^x=0.5
Solve by trial and error to be 0.315±
Respond to this Question
Similar Questions

Math
How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw … 
Calculus
55. Find an equation of the tangent line to the graph of f(x) =x^3  2x + 1 a) at (2,5); b) at (1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x)  (3/2) b) No solution c) No solution For each function, find the points on … 
calculus
is the function f(x)=x^2 increasing on decreasing at x = 1. can anyone please check my reasoning: the value of the derivative of the function at x=1 is 2, so that means the slope of the tangent line to the graph at that is a negative … 
Calculus: for mathmate
Find the slope of the tangent line to the graph of the given function at any point: 1. f(x)= 13 I understand that you said the tangent to the line is the coefficient of x, but what would be the slope of this problem. For problems like … 
Math
Find the points on the graph of the following function where the slope of the tangent line is equal to 5/2. f(x) = x+5/x5 (x, y) = (smaller xvalue) (x, y) = (larger xvalue) 
Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
Calculus
Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = 8/5 x^2 + 7 x + 7;(1, 8/5) slope tangent line y = 
Calculus
Find the slope and equation of the tangent line to the graph of the function at the given value of x. f(x)=x^420x^2+64;x=1 
AP Calc. AB
let f be the function given by f(x)=2e^x^3. F0r what value of x is the slope of the line tangent to the graph of f at (x,f(x)) equal to 6 
calculus
1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?