Equation of Tangent Lines

1. Find an equation of the tangent line to \(f(x) = x^3+4\) at the point \((1, 5)\). Write your final answer in the form \(y = mx + b\).  solution

2. Find an equation of the tangent line to \(f(x) = \frac{3}{4}\, x^4+3x^2-5x+\frac{1}{4}\) at the point \((1, -1)\). Write your final answer in the form \(y = mx + b\).   solution

3. Find an equation of the tangent line to the curve \( y=3+5x-e^x\) at the point \((0, 2)\).  solution

4. Find an equation of the tangent line to the curve \( y=1+xe^x\) at the point \((0, 1)\).   solution