1. Find f ' (-4), if f (x) = (5x2 + 6x) (3x2 + 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values.

2. Find f' (x) for f (x) = - 7x2 + 4x - 10.

14x - 10

-14x + 4

14x + 4

None of these

3. If f and g are differentiable functions for all real values of x such that f (1) = 4, g (1) = 3, f ' (3) = - 5, f ' (1) = - 4, g ' (1) = - 3, g ' (3) = 2, then find h ' (1) if h (x) = f (x) g (x).

-9

-24

0

24

4. Find the coefficient of the squared term in the simplified form for the second derivative, f " (x) for f (x) = (x3 + 2x + 3) (3x3 - 6x2 - 8x + 1). Use the hyphen symbol, -, for negative values.

Question

Mathematics

Leyla Ward

27 December, 03:45

1. Find f ' (-4), if f (x) = (5x2 + 6x) (3x2 + 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values.

2. Find f' (x) for f (x) = - 7x2 + 4x - 10.

14x - 10

-14x + 4

14x + 4

None of these

3. If f and g are differentiable functions for all real values of x such that f (1) = 4, g (1) = 3, f ' (3) = - 5, f ' (1) = - 4, g ' (1) = - 3, g ' (3) = 2, then find h ' (1) if h (x) = f (x) g (x).

-9

-24

0

24

4. Find the coefficient of the squared term in the simplified form for the second derivative, f " (x) for f (x) = (x3 + 2x + 3) (3x3 - 6x2 - 8x + 1). Use the hyphen symbol, -, for negative values.

+3

Answers (1)

Know the Answer?

Alyson Hale · Answer 1

1. Find f ' (-4), if f (x) = (5x^2 + 6x) (3x^2 + 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values.

f (x) = 15x^4 + 35x^2 + 18x^3 + 42x

f' (x) = 15*4 x^3 + 2*35 x + 3*18 x^2 + 42

f' (x) = 60x^3 + 70x + 58x^2 + 42

f' ( - 4) = 60 (-4) ^3 + 70 ( - 4) + 58 (-4) ^2 + 42 = - 3150

Answer: - 3150

2. Find f' (x) for f (x) = - 7x^2 + 4x - 10.

f' (x) = - 2*7x + 4 = - 14x + 4

Answer: - 14x + 4

3. If f and g are differentiable functions for all real values of x such that f (1) = 4, g (1) = 3, f ' (3) = - 5, f ' (1) = - 4, g ' (1) = - 3, g ' (3) = 2, then find h ' (1) if h (x) = f (x) g (x).

h (x) = f (x) g (x) = > h ' (x) =. chain rule = > f ' (x) g (x) + f (x) g ' (x)

h' (1) = f ' (1) g (1) + f (1) g ' (1) = - 4 * 3 + 4 * ( - 3) = - 12 - 12 = - 24

Answer: - 24

4. Find the coefficient of the squared term in the simplified form for the second derivative, f " (x) for f (x) = (x^3 + 2x + 3) (3x^3 - 6x^2 - 8x + 1). Use the hyphen symbol, -, for negative values.

f (x) = 3x^6 - 6x^3 - 8x^4 + x^3 + 6x^5 - 12x^3 - 16x^2 + 2x + 9x^3 - 18x^2 - 24x + 3 = 3x^6 + 6x^5 - 8x^4 - 8x^3 - 34x^2 + 26x + 3

f ' (x) = 18x^5 + 30x^4 - 32x^3 - 24x^2 - 68x + 26

f '' (x) = 90x^4 + 120x^3 - 96x^2 - 48x - 68

So the coefficient of the squared term is - 96.

You can tell that without all the calculus if you realize that the squared term comes from the term with the power 4 (because when you find the second derivative the power decreases two units). And that term is - 8x^4

And the second derivative of - 8x^4 is - 8*4*3 x^2 = - 96x^2, where you see the coefficient is - 96.

Answer: - 96