# What is the instantaneous rate of change for #f(t)= sqrt (5t+1)# when t=1?

##### 1 Answer

Jul 21, 2016

#### Explanation:

The

#color(blue)"instantaneous rate of change"# is the value of f'(t) at t = 1.differentiate f(t) using the

#color(blue)"chain rule and power rule"#

#f(t)=sqrt(5t+1)=(5t+1)^(1/2)#

#rArrf'(t)=1/2(5t+1)^(-1/2).d/dt(5t+1)#

#=5/2(5t+1)^(-1/2)=5/(2(5t+1)^(1/2))=5/(2sqrt(5t+1))#

#rArrf'(1)=5/(2sqrt6)=5/(2sqrt6)xxsqrt6/sqrt6=(5sqrt6)/12#