(1 point) the point p( 0.2 , 20 ) lies on the curve y = 4 / x . let q be the point (x, 4 / x ) . a.) find the slope of the secant line pq for the following values of x. if x= 0.3, the slope of pq is: if x= 0.21, the slope of pq is: if x= 0.1, the slope of pq is: if x= 0.19, the slope of pq is: b.) based on the above results, guess the slope of the tangent line to the curve at p(0.2 , 20 ).

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)