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Consider the following function.g(t) = 4t2 − 1; dgdtwhen  t = 5 (a) Use the limit definition of the derivative (algebraic method) to write an expression for the rate-of-change function of the given function. g'(t) =lim (b) Evaluate the rate of change as indicated. dgdtwhen t = 5  =

Question

Consider the following function.

g(t) = 4t2 − 1; 
dg
dt
when   
t = 5

 

(a) Use the limit definition of the derivative (algebraic method) to write an expression for the rate-of-change function of the given function.
g'(t) =
lim
 


(b) Evaluate the rate of change as indicated.
dg
dt
when  

t = 5  

 
   
check_circleAnswer
Step 1

To solve (a) and (b) on limits

Step 2

Note that the constant term -1 has no...

(a)g() 4-
g') rate of change
= lim g(+h)-g(t)
h
h0
8th+h
lim
4(t+h-4r
lim
h
h0
h0
lim(8t+h) 8t
h0
=
|I
help_outline

Image Transcriptionclose

(a)g() 4- g') rate of change = lim g(+h)-g(t) h h0 8th+h lim 4(t+h-4r lim h h0 h0 lim(8t+h) 8t h0 = |I

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Tagged in

Math

Calculus

Derivative

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