Question

Let the function given by f(x) = 2cosx + 3e^x. What is the value of f’(0)?

A) 2
B) 3
C) 4
D) 5
E) 6

Answer 1

To find the value of f'(0) for the given function, we differentiate the function and substitute x = 0 into the derivative. The value of f'(0) is 3.

Step-by-step explanation:

To find the value of f'(0), we need to differentiate the given function f(x) = 2cosx + 3e^x. The derivative of 2cosx is -2sinx and the derivative of 3e^x is 3e^x (since the derivative of e^x is itself).

Therefore, the derivative of the function f(x) = 2cosx + 3e^x is f'(x) = -2sinx + 3e^x. To find f'(0), we substitute x = 0 into the derivative function:

f'(0) = -2sin(0) + 3e^0
f'(0) = -2(0) + 3(1)
f'(0) = 0 + 3
f'(0) = 3