f(x)=3x^2−2x a) Verify that f'(x)=6x-2 b) Find the instantaneous rate of

Tabansi

Tabansi

Answered question

2021-08-09

f(x)=3x22x
a) Verify that f'(x)=6x-2
b) Find the instantaneous rate of change of f(x) at x=-1

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-08-10Added 98 answers

Given:
f(x)=3x22x
a) f(x)=limh0f(x+h)f(x)h
f(x+h)=3(x+h)22(x+h)
=3(x2+2xh+h2)2x2h
=3x2+6xh+3h22x2h
And since f(x)=3x22x
f(x+h)f(x)=3x2+6xh+3h22x2h(3x22x)
=6xh+3h22h.
f(x+h)f(x)h=6xh+3h22hh=6x+3h2
Now the first equation becomes
f(x)=limh0(6x+3h2)
=6x-2
b) f'(-1)=6(-1)-2=-8
Result:
a) f'(x)=6x-2
b) -8

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