1. (4 pts.) Consider the function f(x) =1-4sinx+3x.e*. (a) (2 pts.) Find the derivative of f(x) at x = 0. (b) (2 pts.) Write an equation of the tangent line to the curve at x = 0. 2. (6 pts.) Differentiate the following. Do not simplify your answers. (a) f(x) = 8secx (b) f (t) = 5+2. (3-2+3)6 (c) f(x) =sin'(5x) 3. (3 pts.) Find the 15th derivative of f (x) = 2x's -3*, fus) (x)- Note: n!=1 . 2 .3 .4 .... .(n-1) . n (n! read "n factorial".) Example: 5!=1 . 2 .3 .4 .5=120 4. (3 pts.) At what point is the tangent line to y =1+ 2e* -3x parallel to 3x - y =5 ? (Note: give exact answer, using logarithms as needed. Find both coordinates of the point.)