Would the first derivative of

Question

R(t)=9t[(t-4)^3/2.718] be R'(t)=3.311258278(3(t-4)^2(t)+(t-4)^3) and the second derivative be
R''(t)=3.311258278(6(t-4)x+6(t-4)^2)?

Answer 1

you can check your results at wolframalpha.com

Just type "derivative" or "2nd derivative" and your function. Check to be sure it interprets your input as you intended. Parentheses are your friend.

For your function, you correctly extracted the 9/e constant, and the derivative of t(t-4)^3 is
3(t-4)^2 + (t-4)^3 = (t-1)(t-4)^2

2nd derivative is 12(t-2)(t-4)

Your answers appear correct