Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3), i) using Definition 1, ii) using Equation 2

Felix Fitzgerald

Felix Fitzgerald

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2022-08-20

Find the slope of the tangent line to the parabola y=4xx2 at the point (1,3), i) using Definition 1, ii) using Equation 2

Answer & Explanation

tkaljegs

tkaljegs

Beginner2022-08-21Added 9 answers

Definition 2:
m=limxaf(x)f(a)xa
i)
m=limx1f(x)f(1)x1
=limx1(4xx2)(4(1)12)x1
=limx1x2+4x3x1
=limx1(x1)(3x)x1
=limx1(3x)=31
=2
Equation 3:
m=limh0f(a+h)f(a)h
ii)
m=limh0f(1+h)f(1)h
=limh0[4(1+h)(1+h)2][4(1)12]h
=limh02hh2h
=limh0(2h)=20
=2
Result:
m=2

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