Find the derivative of the function (PLEASE HELP)

Question

L(t) = -2.3 + 0.24t + 0.0027t^2

 

Question: Find dL/dt for 18 ≤ t ≤ 38, using the limit definition of the derivation and then using differentiation rules. 

Answer 1

Hey! Lets solve this shall we ?

Let the limit as h approaches 0 as

lim [-2.3+0.24t+0.24h+0.0027t²+0.0054th+0.0027h²] - [-2.3+0.24t+0.0027t²] / h

h->0

lim (0.24+.0054t+0.0027h) = 0.24 + 0.0054t

h->0

The derivative is also computed using the power rule of derivation such that

L'(t) = 0 + 0.24 + (2)(0.0027)t = 0.24 + 0.0054t

I hope this helped!