Consider the function f left parenthesis x right parenthesis equals 3 x squared minus 5 x minus 2f (x) = 3x2-5x-2 and complete parts (a) through (c). (a) find f left parenthesis a plus h right parenthesisf (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=44. (a) f left parenthesis a plus h right parenthesisf (a+h) equals = nothing (simplify your answer. do not factor.)

Question

Mathematics

Alfredo

2 July, 01:51

Consider the function f left parenthesis x right parenthesis equals 3 x squared minus 5 x minus 2f (x) = 3x2-5x-2 and complete parts (a) through (c). (a) find f left parenthesis a plus h right parenthesisf (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=44. (a) f left parenthesis a plus h right parenthesisf (a+h) equals = nothing (simplify your answer. do not factor.)

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Alejandra Grant · Answer 1

Given f (x) = 3x²-5x-2

a) To find f (a+h) replace x with a+h in the given function. So,

f (a+h) = 3 (a+h) ²-5 (a+h) - 2

=3 (a²+2ah+h²) - 5 (a+h) - 2 By using the formula (x+y) ²=x²+2xy+y².

=3a²+6ah+3h²-5a-5h-2 By distributing property.

b) Similarly to find f (a) we need to replace x with a. So,

f (a) = 3a²-5a-2

So, f (a+h) - f (h) = (3a²+6ah+3h²-5a-5h-2) - (3a²-5a-2)

=3a²+6ah+3h²-5a-5h-2-3a²+5a+2.

=6ah+3h^2-5h (All other terms has been cancel out)