Compute the indicated derivative.
R(t) = −0.8t2; R'(7)
is that 1.6 to the 7 power
To compute the derivative of the function R(t) = -0.8t^2, we need to use the power rule for differentiation, which states that the derivative of t^n, where n is a constant, is equal to n*t^(n-1).
In this case, since we have R(t) = -0.8t^2, the constant n is 2. Applying the power rule, we differentiate R(t) by multiplying the exponent (2) by the coefficient (-0.8) and subtracting 1 from the exponent. Therefore, the derivative of R(t) is given by:
R'(t) = -0.8 * 2t^(2-1) = -1.6t.
Now, to find R'(7), we substitute t = 7 into the derivative equation:
R'(7) = -1.6 * 7 = -11.2.
Therefore, R'(7) equals -11.2.