Answer:
1/6
Step-by-step explanation:
For f(x) = e^(5x) +x, the derivative is ...
f'(x) = 5e^(5x) +1
Then the linearization at x=0 is ...
f(x) ≈ f'(x)(x -0) + f(0)
f(x) ≈ 6x +1
Then for f(x) = 2, we have
6x +1 = 2
x = (2 -1)/6 = 1/6
So, an approximate value of x is x = 1/6.
_____
As exponential functions do, the curve grows steeper very quickly, so this value of x is an overestimate.
