Question

Estimate the values of s'(15) and s'(25) and interpret them as:

a) Tangent slopes at points 15 and 25
b) Area under the curve at points 15 and 25
c) Instantaneous rates of change at points 15 and 25
d) Maximum values at points 15 and 25

Answer 1

To estimate the values of s'(15) and s'(25), we need to find the tangent line to the curve at t = 15 s and t = 25 s. Plugging the corresponding positions into the slope equation gives us the values of s'(15) and s'(25).

Step-by-step explanation:

The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. To estimate the values of s'(15) and s'(25), we need to find the tangent line to the curve at t = 15 s and t = 25 s. The tangent line at t = 15 s corresponds to a position of 1,300 m at time 19 s and a position of 3,120 m at time 32 s. Plugging these values into the equation for slope, we can determine the values of s'(15) and s'(25).