calculus need help please

Question

5. Use Linear Approximation to estimate . Provide your answer in 2 decimal places.  Do not use a calculator. Show work for credit.

Answer 1

Let f(x) = e^x, f'(x)= e^x

to approximate for f(-0.01) use x = 0

f(0) = 1

f'(0) = 1 = m

y-y₀ = m(x-x₀) use (x₀,y₀) = (0,1)

f(x) = y = x + 1

f(-0.01) = -0.01 + 1 = 0.99