Find the indicated difference quotient and simplify your answer. NSK PSKf(x)=x^3+3x\ \frac{f(x+h)-f(x)}{h}ZSK,

jubateee

jubateee

Answered question

2021-12-09

Find the indicated difference quotient and simplify your answer.
f(x)=x3+3x f(x+h)f(x)h, h does not equal 0
f(x)=1x2, g(x)g(3)x3, x does not equal 3.
f(t)=1t2, f(t)f(1)t1, t does not equal 1.

Answer & Explanation

kalfswors0m

kalfswors0m

Beginner2021-12-10Added 24 answers

Using given f(x) first find f(x+h).
f(x)=x3+3x
f(x+h)=(x+h)3+3(x+h)
f(x+h)=x3+3x2h+3xh2+h3+3x+3h
Plugged the expression of f(x) and f(x+h) in the difference quotient and simplified.
f(x+h)f(x)h
=(x3+3x2h+3xh2+h3+3x+3h)(x3+3x)h
=3x2h+3xh2+h3+3hh
=h(3x2)+3xh+h2+3h
=3x2+3xh+h2+3
Answer: =3x2+3xh+h2+3

temzej9

temzej9

Beginner2021-12-11Added 30 answers

Using given g(x) first find g(3)
g(x)=1x2
g(3)=132
g(3)=19
Plugged the expression of g(x) and g(3) in the difference quotient and simplified.
g(x)g(3)x3
=1x219x3
=9x29x2x3
=9x29x2(x3)
=(3+x)(3x)9x2(x3)
=(x+3)9x2
Answer: =(x+3)9x2

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