Finding the equation of a tangent to a curve that has the least slope.

Find an equation of the tangent line to the curve Y= x3 - 3x2 + 5x that has the least slope.

Finding the tangent to a curve. Picture included.

Find an equation of the tangent line to the curve Y= x3 - 3x2 + 5x that has the least slope.

Derivatives from first principles using standard theorems on trigonometric limits.

Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).

Implicit differentiation : the chain rule and product rule.

Use implicit differentiation to find dy/dx if y^2 + 3xy + x^2 + 10 = 0 (1) where y is a function of the independent variable x.

Finding the derivative of the tangent function by an application of the quotient rule.

Using the quotient rule, obtain an expression for the derivative of tan(x). State the values for which this is well-defined.

Maclaurin Series

I am trying to find the Maclaurin series for the function f(x) = sin2x/3x.

Power Series Representation

I am trying to figure out a powers series representation for the function f(x) = e^x, centered at c = -2. I also need to find the interval of convergence.

power series

I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also c ...continues

Implicit Differentiation

Find y" for x^2/a^2 - y^2/b^2 = 1

Extending power series.

Extend e^(x) into a power series at center x=1