Find the equation of the tangent line of the function f at the point (4,f(4)) Us

Question

Find the equation of the tangent line of the function f at the point (4,f(4)) Use differentials to estimate the value of f(4.02). Use implicit differentiation to prove that the curve x' ~y' - (2x'+2y -x) (see exercise 27 of page 187 of the textbook) has a vertical tangent line at the point (1,0). One side of a right triangle is known to be 25 cm exactly. The angle opposite to this side is measured to be 60% with a possible enor of plusminus 0.5'. Use differentials to estimate the errors in the adjacent side and the hypothenuse. Estimate the percentage errors in the adjacent side and hypothenuse.

Explanation / Answer

6)

f(x)=(x-1)/x

f(x)=x -(1/x)

f(x)=x1/2 -x-1/2

f(4)=41/2 -4-1/2

f(4)=2-(1/2)

f(4)=3/2

f '(x)=(1/2)x-1/2 +(1/2)x-3/2

f '(4)=(1/2)4-1/2 +(1/2)4-3/2

f '(4)=(1/4) +(1/16)

f '(4)=5/16

f(4.02)= f(4) +f '(4)*(4.02-4)

f(4.02)= (3/2) +((5/16)*(0.02))

f(4.02)=1.50625

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