Question

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the forumula: f') = -3(0)6 +SO) If there is 4 grams of solid at timet +2 estimat nate the Question Help: Message instructo Submit Question

Answer 1

of a function is differentiable at t=a. the expression f(a) = f'(a) (t-a) is a lineas approxmation of the function. We are working with a differentiable function because its derivative is defined. It is given ab f'(t) = - 3 ft (6+ f(t)). We also know that f(2)=4 and we need to estimate the value of the function 1 second to minutes later, . f (2+ 8) = f ( 12 ) we can use a linear approximation of the functions around the point (2, 4) and then evaluate the appoximation 121 fCH) f(2) + f'(2) (+-2) f(2) +(-3 f®) (6+f>))) (+-2) ř 4 + (-3.4 (6+4)) (+-2) ~ 4 - 120 (+-2) f(121) ~ 4 - 120 (121 - 2) 4 - 120 x 1 72 The appoximate amound of solid 1 second later will be [2grams 121 60