I am in a calculus class and am stuck on two problems that have something to do with derivatives. I think im on the right trak when starting them but tend to fall of when getting to the expanded portions of the problem. Maybe im making them harder than they really are, but here are the two problems:
1.) Car A is traveling at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 mi and car B is 0.4 mi from the intersection?
2.) The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0) = 2, f'(0) = -4, and f"(0) = 3.
A.) The function g is given by g(x) = e^ax + f(x) for all real numbers, where a is a constant. Find g'(0) and g"(0) in terms of a.
B.) The function h is given by h(x) = cos(kx)*f(x) for all real numbers, where k is a constant. Find h'(x) and write an equation for the line tangent to the graph of h at x = 0
Problem #2 I think I have right, but being able to compare with someone elses work would be good, that way I can see what I may have did wrong or could have done differently. Thanks for any help you all can give
' = Derivative.
" = Double Darivative.