Question

Compute the indicated derivative U(t) = 5.1t^2 − 1.7t; U'(6)

Answer 1

To compute U'(t) for U(t) = 5.1t^2 - 1.7t at t = 6, take the derivative to get U'(t) = 10.2t - 1.7, then substitute t = 6 to find U'(6) = 59.5.

Step-by-step explanation:

To compute the indicated derivative U'(t) of the function U(t) = 5.1t2 − 1.7t at t = 6, we need to first take the derivative of U(t) with respect to t. Applying the power rule for differentiation, the derivative U'(t) is 2 × 5.1t - 1.7. Now we substitute t = 6 into this derivative to find U'(6).

The calculation steps are as follows:

• Find the derivative: U'(t) = 2 × 5.1t - 1.7 = 10.2t - 1.7
• Substitute t = 6: U'(6) = 10.2 × 6 - 1.7 = 61.2 - 1.7 = 59.5
  

Therefore, the value of U'(6) is 59.5.

Answer 2

Answer: 59.5

Step-by-step explanation:

U(t) = 5.1t^2 − 1.7t

U'(t)=2*5.1t-1.7

U'(t)=10.2t-1.7

U'(6)=10.2(6)-1.7

U'(6)=61.2-1.7

U'(6)=59.5