GIVING 10 POINTS if you help me with these calculus exercises
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GIVING 10 POINTS if you help me with these calculus exercises

[From: ] [author: ] [Date: 12-05-30] [Hit: ]
f(x + h) = (x + h)^2 + 6(x + h) - 10f(x)= lim(h->0) [f(x + h) - f(x)] / h= lim(h->0) [((x + h)^2 + 6(x + h) - 10) - (x^2 + 6x - 10)] / h= lim(h->0) [x^2 + 2xh + h^2 + 6x + 6h - 10 - x^2 - 6x + 10] / h= lim(h->0) [2xh + h^2 + 6h] / h= lim(h->0) 2x + h + 6= 2x + 0 + 6= 2x + 64)f(x) = 2x^2 - 7x + 3, f(x + h) = 2(x + h)^2 - 7(x + h) + 3f(x)= lim(h->0) [f(x + h) - f(x)] / h= lim(h->0) [(2(x + h)^2 - 7(x + h) + 3) - (2x^2 - 7x + 3)] / h= lim(h->0) [2x^2 + 4xh + h^2 - 7x - 7h + 3 - 2x^2 + 7x - 3] / h= lim(h->0) [4xh + h^2 - 7h] / h= lim(h->0) 4x + h - 7= 4x + 0 - 7= 4x - 75)f(x) = -x^2 + 4x - 9,......
Find derivative using the four-step process to find f ' (x) (<---------THIS IS THE HARD PART)
then i have to find f ' (5) and f ' (6) (you don't need do this part, i know how to do it)

1- f(x) = -5
2- f(x) = 2 - 3x^2
3- f(x) x^2 + 6x - 10
4- f(x) = 2x^2 - 7x +3
5- f(x) = -x^2 + 4x - 9
6- f(x) = 2x^3 + 1
7- f(x) = 4 + 4/x
8- f(x) = 5 + 3√x
9- f(x) = 10 √x+5
10- f(x) = 3x /x+2

PLEASE, SHOW PROCESS

FORMULA FOR THE FOUR-STEP PROCESS: F(x+h) - f(x) / h

-
1)

f(x) = -5, f(x + h) = -5

f'(x)
= lim(h->0) [f(x + h) - f(x)] / h
= lim(h->0) [(-5) - (-5)] / h
= lim(h->0) [-5 + 5] / h
= lim(h->0) 0 / h
= lim(h->0) 0
= 0

2)

f(x) = 2 - 3x^2, f(x + h) = 2 - 3(x + h)^2

f'(x)
= lim(h->0) [f(x + h) - f(x)] / h
= lim(h->0) [(2 - 3(x + h)^2) - (2 - 3x^2)] / h
= lim(h->0) [2 - 3(x^2 + 2xh + h^2) - 2 + 3x^2] / h
= lim(h->0) [2 - 3x^2 - 6xh - 3h^2 - 2 + 3x^2] / h
= lim(h->0) [-6xh - 3h^2] / h
= lim(x->0) -6x - 3h
= -6x - 3(0)
= -6x - 0
= -6x

3)

f(x) = x^2 + 6x - 10, f(x + h) = (x + h)^2 + 6(x + h) - 10

f'(x)
= lim(h->0) [f(x + h) - f(x)] / h
= lim(h->0) [((x + h)^2 + 6(x + h) - 10) - (x^2 + 6x - 10)] / h
= lim(h->0) [x^2 + 2xh + h^2 + 6x + 6h - 10 - x^2 - 6x + 10] / h
= lim(h->0) [2xh + h^2 + 6h] / h
= lim(h->0) 2x + h + 6
= 2x + 0 + 6
= 2x + 6

4)

f(x) = 2x^2 - 7x + 3, f(x + h) = 2(x + h)^2 - 7(x + h) + 3

f'(x)
= lim(h->0) [f(x + h) - f(x)] / h
= lim(h->0) [(2(x + h)^2 - 7(x + h) + 3) - (2x^2 - 7x + 3)] / h
= lim(h->0) [2x^2 + 4xh + h^2 - 7x - 7h + 3 - 2x^2 + 7x - 3] / h
= lim(h->0) [4xh + h^2 - 7h] / h
= lim(h->0) 4x + h - 7
= 4x + 0 - 7
= 4x - 7

5)

f(x) = -x^2 + 4x - 9, f(x + h) = -(x + h)^2 + 4(x + h) - 9

f'(x)
= lim(h->0) [f(x + h) - f(x)] / h
= lim(h->0) [(-(x + h)^2 + 4(x + h) - 9) - (-x^2 + 4x - 9)] / h
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