2 years ago
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
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Best Answer
jeffdunhamticketseugene Staff answered 2 years ago
jeffdunhamticketseugene Staff answered 2 years ago
Definition 2:
m=lim_(x-> a)(f(x)-f(a))/(x-a)
i)
m=lim_(x-> 1)(f(x)-f(1))/(x-1)
=lim_(x-> 1)((4x-x^(2))-(4(1)-1^(2)))/(x-1)
=lim_(x-> 1)(-x^(2)+4x-3)/(x-1)
=lim_(x-> 1)((x-1)(3-x))/(x-1)
=lim_(x-> 1)(3-x)=3-1
=2
Equation 3:
m=lim_(h-> 0)(f(a+h)-f(a))/(h)
ii)
m=lim_(h-> 0)(f(1+h)-f(1))/(h)
=lim_(h-> 0)([4(1+h)-(1+h)^(2)]-[4(1)-1^(2)])/(h)
=lim_(h-> 0)(2h-h^(2))/(h)
=lim_(h-> 0)(2-h)=2-0
=2
Result:
m=2