181 Tangents and Velocities: Problem 1 Previous Problem Problem List Next Proble

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181 Tangents and Velocities: Problem 1 Previous Problem Problem List Next Problem (I point) The point P(3,19)lies on the curve y-z2 +z+7/fQis the point (z, z2+7), find the slope of the secant line poor the following values of z If z = 3.1, the slope of PQ is: and if z -3.01, the slope of PQ is: and if z = 2.0, the slope of PQ is. and if Z = 2.09, the slope of PQ is Based on the above results, guess the slope of the tangent line to the curve at P(3, 19) Note: You can earn partial credt on this problem Preview My Answers Submit Answers You have attempted this problem 2 times Your overall recorded score is 0% You have unlimited attempts remaining

Explanation / Answer

When x= 3.1, then

slope of PQ = f(3.1) -f(3)/(3.1 -3) = (19.71 -19)/(3.1 -3) =7.1

When x= 3.01, then

slope of PQ = f(3.01) -f(3)/(3.01 -3) = (19.0701 -19)/(3.01 -3) =7.01

When x=2.9, then

slope of PQ = f(2.9) -f(3)/(2.9 -3) = (18.31 -19)/(2.9 -3) =6.9

When x=2.99, then

slope of PQ = f(2.99) -f(3)/(2.99 -3) = (18.9301 -19)/(2.99 -3) =6.99

Based on the result, slope of tangent line is 7

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