The answer to your question would be 6.3
Answer:
exact form - b = -11/5
decimal form - b = -2.2
Mixed number form - b = -2 1/5
For this question the answer would be x=-3 and x=-2
First of all, recall that y is a product of function of x. We have three factors:
![f(x)=x^2,\quad g(x)=e^{3x},\quad h(x)=\sin(4x)](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2C%5Cquad%20g%28x%29%3De%5E%7B3x%7D%2C%5Cquad%20h%28x%29%3D%5Csin%284x%29)
The derivative of a product of function is computed by deriving one function at the time, and then adding all the results:
![y' = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)](https://tex.z-dn.net/?f=y%27%20%3D%20f%27%28x%29g%28x%29h%28x%29%2Bf%28x%29g%27%28x%29h%28x%29%2Bf%28x%29g%28x%29h%27%28x%29)
Let's compute the derivative of each function first:
![f'(x)=2x,\quad g'(x) = 3e^{3x},\quad h'(x)=4\cos(4x)](https://tex.z-dn.net/?f=f%27%28x%29%3D2x%2C%5Cquad%20g%27%28x%29%20%3D%203e%5E%7B3x%7D%2C%5Cquad%20h%27%28x%29%3D4%5Ccos%284x%29)
Now plug f, f', g, g', h, h' in the formula above as required:
![2xe^{3x}\sin(4x)+3x^2e^{3x}\sin(4x)+4x^2e^{3x}\cos(4x)](https://tex.z-dn.net/?f=2xe%5E%7B3x%7D%5Csin%284x%29%2B3x%5E2e%5E%7B3x%7D%5Csin%284x%29%2B4x%5E2e%5E%7B3x%7D%5Ccos%284x%29)