Use linear approximation, i. e. the tangent line, to approximate √16.4 as follows: Let f(x)=√x. Find the equation of the tangent line

Step-by-step explanation:

The equation for a tangent line of f(x) in the point (a,f(a)) can be calculated as:

L(x) = f(a) + f'(a)(x-a)

Where L(x) is also call a linear approximation and f'(a) is the value of the derivative of f(x) in (a,f(a)).

So, the derivative of f(x) is:

Then, to find the linear approximation we are going to use the point (16, f(16)). So a is 16 and f(a) and f'(a) are calculated as:

Then, replacing the values, we get that the equation of the tangent line in (16,4) is:

Finally, the approximation for is:

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

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