Recall that, given a differentiable function f and a point a in the domain of f,
ID: 2846761 • Letter: R
Question
Recall that, given a differentiable function f and a point a in the domain of f, the linear approximation L(x) to f(x) at the point x=a is given by quadquad displaystyle L(x) = f(a) + f^prime(a)(x-a). A linear approximation is useful because of its simplicity and the fact that it may be used to approximate f(x) for values of x near a. That is, quadquad f(x) pprox L(x), for x near a. Find the linear approximation , L(x); to the function ,displaystyle f(x) = 4 x^2 + 8 x ; at the point , displaystyle x=2 , and use it to estimate the value of displaystyle fleft( rac{18}{10} ight). L(x) = displaystyle fleft( rac{18}{10} ight) pprox
Explanation / Answer
f(18/10) = f(2)-((2-1.8) f'(2)
= 32-(.2*24)
= 27.2
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