The displacement (in meters) of a particle moving in a straight line is given by

Question

The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 9t + 15, where C is measured in seconds. Fine the average velocity over each time interval. Find the instantaneous velocity when t = 4. m/s Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = -4 and g'(5) = 3. (Enter your answer as an equation in terms of y and x.) If f(X) = 8x2 - x3, find f'(1) and use it to find an equation of the tangent line to the curve y = 8x2 - x3 at the point (1, 7).

Explanation / Answer

S(t)=t2-9t+15

Avg. velocity on time interval (t1,t2) = S(t2)-S(t1)/(t2-t1)

a)[3,4] Avg. vel. =S(4)-S(3)/(4-3) = -2

similarly you can do for other ones.

b)Instantaneous velocity = dS/dt = 2t-9

at t=4 dS/dt=-1 m/s

........................................................................

3. equation of tangent

y-g(5)=g'(5)(x-5)

y+4=3(x-5)

y=3x-19

..........................................................................

4.f(x)=8x2-x3

f'(x)=16x-3x2

f'(1)=13

equation of tangent

y-7=13(x-1)

y=13x-6

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