Determine the equation of the tangent line to the function 𝑓(𝑥) = 4^x , at x=1. EXACT VALUES REQUIRED.

Question

Determine the equation of the tangent line to the function 𝑓(𝑥) = 4^x

, at x=1. EXACT

VALUES REQUIRED.

Answer 1

f(x)= 4^x

at x=1

f(1) = 4^1 = 4

that's the point (1,4)

find the tangent line through that point

where f'(1) = the tangent line's slope= m =ln4(4^x)

f'(1) = ln4(4^1) = 4ln4

y=mx + b= equation of the tangent line in slope intercept form, b=intercept, m=slope

4=m(1) +b

b = 4-m =4-4ln4

y=4(ln4)x +4-4ln4