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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.

Respuesta :

Answer:

613

Step-by-step explanation:

Given that

[tex]f(x)=4x^2-3x-1[/tex]

Substitute a+h for x

[tex]f(a+h)=4(a+h)^2-3(a+h)-1[/tex]

[tex]f(a)=4a^2-3a-1[/tex]

[tex]f(a+h)-f(a) = 4(a^2+2ah+h^2)-3(a+h)-1 - (4a^2-3a-1)\\= 8ah+4h^2-3h[/tex]

Divide by h and take limit as h tends to 0

we get

[tex]f'(x) = 8x-3[/tex]

c) Instantaneous rate of change

= f'(x)

when a = 77

we get

[tex]8(77)-3\\=613[/tex]

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