Tangent Line to an Exponential Function

Question

Let f(x) = 10x+9-19e^x. Find the equation of the tangent line to the graph of f(x) at the point (0,-10).

Answer 1

f'(x)  = 10  + 19 e^x

 

f'(0) =  10  + 19 e⁰ = 10  + 19  =  29

 

y  =  mx + b  = 29x +  b

 

So -10  =  0 x  +  b   so b =  -10

 

The equation of the tangent line is

 

y  =  29 x  -  10