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
