Respuesta :
Answer:
m = (4/x - 20)/(x - 0.2) = 4(1-5x)/x(x-0.2)
x= 0.3 | m = -66.67
x= 0.21 | m = -95.24
x= 0.1 | m = -200
x= 0.19 | m = -105.26
slope of P = -100
Step-by-step explanation:
P( 0.2 , 20 ) ∈ y = 4 / x .
Q(x, 4 / x ) .
a.) Find the slope of the secant line PQ for the following values of x.
slope: m = (y₂-y₁)/(x₂-x₁)
m = (4/x - 20)/(x - 0.2) = 4(1-5x)/x(x-0.2)
If x= 0.3, the slope of PQ is: [4(1-5.0.3)]/[0.3(0.3-0.2)] = -66.67
If x= 0.21, the slope of PQ is: [4(1-5.0.21)]/[0.21(0.21-0.2)] = -95.24
If x= 0.1, the slope of PQ is: [4(1-5.0.1)]/[0.1(0.1-0.2)] = -200
If x= 0.19, the slope of PQ is: [4(1-5.0.19)]/[0.19(0.19-0.2)] = -105.26
b.) Based on the above results, guess the slope of the tangent line to the curve at P(0.2 , 20).
Based on the results, if the slope for 0.21 is -95.24 and for 0.19 is -105.26, a difference of 10 units, as 0.2 is in the middle, it would be a difference of 10/2, so -100.
(we can confirm it using derivative and it is -100)
