Derivatives

The motion of a particle is given by  x(t) = -4.9t^2 + 12t +1.  When is the particle at rest?

Determine the slope of a line tangent to f(x) = 3x^2 - 5x  at  x = -1/2

Determine the value of  x  where a line tangent to  f(x) = 5x  has a slope of  -2.

Determine where f(x) = x^3 + 3x^2 - 9x + 1  has a horizontal tangent.

Can the function  f(x) = (2x + 3)^2  be derived using Product Rule?

Find  f '' (x)  for  f(x) = -3x^5 + 11x - 3x^2 + 5.

The position of an object:  x(t) = t^3 + 5t^2 - 8t + 4.  Find position when object is at rest .

Determine the slope of the line tangent to  f(x) = (2x + 3)(x - x^2)  at  x = -1.

An object's height is modeled by s(t) = -4.9t^2 + 12t + 1. When will the object hit the ground?

Determine the slope of a line tangent to  f(x) = 2x(x^2 - 1)  at  x = 3.