MATH SOLVE

2 months ago

Q:
# (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 ).

Accepted Solution

A:

Answer:m = (4/x - 20)/(x - 0.2) = 4(1-5x)/x(x-0.2)x= 0.3 Β | m = -66.67x= 0.21 | m = -95.24x= 0.1 Β | m = -200x= 0.19 | m = -105.26 slope of P = -100Step-by-step explanation: P( 0.2 , 20 ) β y = 4 / x . Q(x, 4 / x ) . a.) Find the slope of the secant line PQ for the following values of x. slope: m = (yβ-yβ)/(xβ-xβ)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)] = -66.67If x= 0.21, the slope of PQ is: [4(1-5.0.21)]/[0.21(0.21-0.2)] = -95.24If x= 0.1, the slope of PQ is: [4(1-5.0.1)]/[0.1(0.1-0.2)] = -200If 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)