Write an equation of the tangent line to the curve traced by r(t) = ti + ((t^(2)/ 2) + 3)j + 2tk at the point corresponding to t = 2

Find the slope of the tangent to the graph of f(x) = x^2 + 1 at the point (2, 5).  Use the method of finding the slope of the secant between (2, 5) and a neighboring point, and moving the neighboring point closer and closer to (2, 5).  What is important here is the method, not the answer, so show your work very clearly.  A diagram is needed, but you do not need to draw all your secant lines if that becomes difficult.

Determine the point on the curve where the slope of tangent line to the curve is 0 or -3 a) f(x)= 2x² - x +1

Find the equation of the tangent line to the curve y 2 sin x at the point (-, 1). The equation of this tangent line can be written in the form = mx + b where т — and b :