Find the equation of the tangent line to the curve:

Question

1. Find the equation of the tangent line to the curve f(x)=2^x at the point P(0,1) is:

Answer 1

f'(x) = the derivative of 2^x = ln2(2^x)

f'(0) = ln2(2^0) = ln2 = slope of the tangent line at the point (0,1)

y= xln2 + b is the equation of the tangent line. solve for b by plugging in the point (0,1)

1 = 0 + b

b = 1

y = xln2 + 1 is the tangent line to the curve at the given point

Answer 2