The equation e^(4x) + x=2 has a solution near x=0. by replacing the left side of the equation by its linearization, find an approximate value for the solution.

**write the exact answer**
x=

Using the linearization mehod, find f'(x) if f(x)=e^(4x)+x, f(x) is approximately =mx+b where m=f'(0). We want to know the value of the x and y intercepts, so we substitute them with 0(vice versa), we will get (0,f(0))=(0,1)

Solve for  x:

f'(x)=(4x)'e^(4x)+(x)'

(4x)'=4 (x)'=1

f'(x)= 5

solve for b:

e^0=1

1= 0+b

b=1

so the approximation for f(x) is y=5x+1

Solve for y, so you substitute the values of x and b

5x+1=2 -1 -1

5x=1 x=1/5

so exact answer is x= 0.2

i would need to see the dot plot : )

on monday rodney ate 1/4th of the sandwich = 3/12

on tuesday he ate 1/3rd of the sandwich = 4/12

therefore in total he has eaten = 3/12 + 4/12 = 7/12

thus we can say that he has eaten 7/12 of the sandwich on monday and tuesday alltogether.

happy to

pls mark as brainliest.