estimate the slope of the tangeant line to the curve at P(9,7)

Question

The point P(9,7) lies on the curve y= √x +4. Let Q be the point (x,√x+4)

if x is 9.1, the slope of PQ is 0.166206

if x= 9.01, the slope of PQ is 0.16662

if x= 8.9, the slope of PQ is 0.1671323

if x= 8.99, the slope of PQ is 0.166713

Based on the above results, estimate the slope of the tangeant line to the curve at p(9,7)

Answer 1

Based on the above we can see the slope is approaching 0.16666666... which is equal to 1/6.

Which you can verify using calculus.