In: Math
If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________
Given the function: y=sin(4x)+e^-3x and dx/dt = 3 when x=0. Then dy/dt = ________________ when x=0.
Let f(x) = ln (√x). The value of c in the interval (1,e) for which f(x) satisfies the Mean Value Theorem (i.e f'(c)= f(e)-f(1) / e-1 ) is: _________________________
Suppose f(x) is a piecewise function: f(x) = 3x^2 -11x-4, if x ≤ 4 and f(x) = kx^2-2x-1, if x >4. Then the value of k that makes f(x) continuous at x=4 is: ______________________