Find the equation of the line normal to the curve y=3x³5x at the point (1,2). Sketch the curve and normal line.

Find an equation for the line tangent to the curve y=x²+3 at the point (1,4). Sketch the curve and the tangent line.

A bullet is fired vertically upward in a controlled test environment. Its distance s(in ft) above the ground is given by s=2600t16.1t², where t is the time(in s). Find the acceleration of the bullet.

The displacement s(in m) of an object is given by the following function of time t(in s).

s(t)=t²+2t

Find theobject's acceleration when t=2.

Evaluate the derivative of the following function at the given point.

xy²+4x²3y²+109=0; (2,5)