Please read the following details for the math problems.?

Question

1) If f(x) = 4x^2 - 3x + 7, find the instantaneous rate of change of f(x) at x = 4 using the Derivative power rule.

2) Find the derivative of f(x) = (6x^3 - x)(10 - 20x)

3)Find the derivative of the function f(x) = (x^2 +1)^3

Does anyone know how to help me with these three stat problems?thanks.

Answer 1

1). The derivative of f(x) is 8x-3.
At x=4, the value of the derivative is 8*4-3, or 29.
That's your instantaneous rate of change.

2). First, multiply out the parentheses.
f(x) = -120x^4 + 60x^3 + 20x^2 -10x
Then take the derivative.
f'(x) = -480x^3 + 180x^2 + 40x -10

3). There are a couple ways to do this, but the simplest is by multiplying out the parentheses.
(x^2 + 1) * (x^2 + 1) * (x^2 + 1)
(x^4 + 2x^2 + 1) * (x^2 + 1)
x^6 + 3x^4 + 3x^2 + 1
Then take the derivative.
f'(x) = 6x^5 + 12x^3 + 6x

Hopefully that helps!

Answer 2

1) 1st derivative: 8x-3 at x=4 29
2) -20 (6x^3-x)+ (18x^2-1)(10-20x)

3) 3( x^2+1)^2 * 2x = 6x^5 + 12 x^3 + 6x

Answer 3

f'(x) = 8x - 3
f'(4) = 8(4) - 3
f'(4) = 32 - 3
f'(4) = 29

----------------------------

f(x) = (6x^3 - x)(10 - 20x)

f'(x) = (6x^3 - x)'(10 - 20x) + (6x^3 - x)(10 - 20x)'
f'(x) = (18x^2 - 1)(10 - 20x) + (6x^3 - x)(-20)
f'(x) = (180x^2 - 360x^3 - 10 + 20x) - 120x^3 + 20x
f'(x) = 180x^2 - 360x^3 - 10 + 20x - 120x^3 + 20x
f'(x) = -480x^3 + 180x^2 + 40x - 10

-------------------------------------------------

f(x) = (x^2 + 1)^3
f(x) = (x^2 + 1)(x^2 + 1)(x^2 + 1)
f(x) = (x^4 + x^2 + x^2 + 1)(x^2 + 1)
f(x) = (x^4 + 2x^2 + 1)(x^2 + 1)
f(x) = x^6 + x^4 + 2x^4 + 2x^2 + x^2 + 1
f(x) = x^6 + 3x^4 + 3x^2 + 1

f'(x) = 6x^5 + 12x^3 + 6x

Answer 4

1) 8x - 3 ----> = 29

2) = -480x^3 + 180x^2 + 40x - 10

3) 6x^5 + 12x^3 + 6x

For number 3, I used the chain rule.

Also, here's the power rule:

d/dx x^n = nx^(n-1)

Here's the chain rule:

df/dx = df/dg * dg/dx

Answer 5

i personally am not very good with higher math. here is a site that might be able to help.

www.math.com

good luck. blessed be.