Question

Consider the function f left parenthesis x right parenthesis equals 4 x squared minus 3 x minus 1f(x)=4x2−3x−1 and complete parts​ (a) through​ (c).​(a) Find f left parenthesis a plus h right parenthesis f(a+h)​;​(b) Find StartFraction f left parenthesis a plus h right parenthesis minus f left parenthesis a right parenthesis Over h EndFraction f(a+h)−f(a) h​;​(c) Find the instantaneous rate of change of f when aequals=77.

Answer 1

Answer:

613

Step-by-step explanation:

Given that

$f(x)=4x^2-3x-1$

Substitute a+h for x

$f(a+h)=4(a+h)^2-3(a+h)-1$

$f(a)=4a^2-3a-1$

$f(a+h)-f(a) = 4(a^2+2ah+h^2)-3(a+h)-1 - (4a^2-3a-1)\\= 8ah+4h^2-3h$

Divide by h and take limit as h tends to 0

we get

$f'(x) = 8x-3$

c) Instantaneous rate of change

= f'(x)

when a = 77

we get

$8(77)-3\\=613$