instantaneous velocity

a.) t0 = 1

[f(t)- f(t0)] / [ t - t0 ] =  

[√(4t)  - √ (4*1)] / [t - 1]  =

[ √(4t) - √(4)] / [ t - 1]  =

[ 2 √(t) - 2] / [t - 1]  =

2 [√(t) - 1] / [t - 1]  =

2[√(t) - 1] / [ (√(t) - 1) (√(t) + 1) ]  =

2 / (√(t) + 1)                     

b.) t0= 4

[√(4t)  - √ (4*4)] / [t - 4] =

[ √(4t)  - √(16)] / [ t - 4] =

[ 2 √(t) - 4 /  [t - 4]  =

2 [√(t)  - 2] / [t - 4]  =

2 [√(t)  - 2] /   [ (√(t)  - 2) (√(t)  + 2) ] =

2 / (√(t)  + 2)   

In part B, how did you split the bottom x-4 into (x+2)(x-2)

I thought you could only do that if it was (x-4)^2?

Note, Yura_chan......

t - 4     can be factored  as

(√(t)  - 2) (√(t)  + 2) 

Because

√(t) * √(t)   - 2√(t)  + 2√(t)  (-2)*(+2)   =

t  -  4