Question

For what values of x does the graph of f(x) = x² sin(x) have a horizontal tangent?

Answer 1

To find the values of x for which the graph of f(x) = x² sin(x) has a horizontal tangent, we need to find the critical points of the function where the derivative is equal to zero.

Step-by-step explanation:

To find the values of x for which the graph of f(x) = x² sin(x) has a horizontal tangent, we need to find the critical points of the function where the derivative is equal to zero. Let's start by finding the derivative of the function:

f'(x) = (2x)(sin(x)) + (x²)(cos(x))

Setting this derivative equal to zero and solving for x, we get:

(2x)(sin(x)) + (x²)(cos(x)) = 0

There is no algebraic solution for this equation, so we need to find the values of x using numerical methods such as graphing or approximation techniques.