Holiday Blog # 1

I already did this blog about 2 weeks ago, but I'm just going to post it again with the Holiday Blog title.

This week we didn't learn anything new in Calculus. All we did was review packets for the exam the whole week. JOYYY TO THE WORLD. Anyway, I guess I'll give a few examples of problems from the ginormous packets we received, and what might possibly be on the exam. >.>

1. Find the slope m of the line tangent to the graph of the function g(x) = 5 - x^2 at the point (2,1).

To do this, you must find the derivative, then plug in your x-value.

Derivative = -2x

Plug in: -2 (2) = -4

The slope is -4

2. Find the slope of the graph of the function at the given value.

f(x) = 2 (4x + 6)^2 when x = 5

Find the derivative and then plug in.

Derivative:

2 * (2 (4x + 6)) * 4

16(4x + 6)

16(4(5) + 6)

16(20 + 6)

16 (26) = 416

416 is the slope of the graph.

3. Find the derivative of the function f(x) = 4x^5 sin x + 5x^9 cos x

(4x^5)(cos x) + (20x^4)(sin x) + (5x^9)(-sin x) + (45x^8)(cos x)

sin x (20x^4 - 5x^9) + cos x (45x^8 + 4x^5)

So, the derivative equals

f ' (x) = (20x^4 - 5x^9)sin x + (4x^5 + 45x^8) cos x