Linear Approximations and Applications # 2

Question

Use linear approximation, i.e. the tangent line, to approximate 4.7^3 as follows:

Let f(x) = x^3. Find the equation of the tangent line to f(x) at x = 5.

L(x) = ______

Using this, we find our approximation for 4.7^3 = ______ (Plug into above equation found.)

Please show steps in written form.

Answer 1

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

a=5

f(x)=x³

f'(x)=3x²

L(4.7)= 5³+3(5)²(4.7-5)

You can finish the arithmetic