Given:
[tex]f(x)=12x+2-11e^x[/tex]
We will find the equation of the line tangent to f(x) at the point (0, -9)
the slope of the tangent line = the first derivative f'(x)
the first derivative will be as follows:
[tex]f^{\prime}(x)=12-11e^x[/tex]
substitute x = 0 to find the slope of the line tangent at (0,-9)
[tex]m=f^{\prime}(0)=12-11e^0=12-11=1[/tex]
So, the equation of the line will be: y = x - 9
so, the answer will be:
m = 1
b = -9
