# Search results for query: *

1. ### Find the local extrema then classify them

Thank you for the suggestion
2. ### Find the local extrema then classify them

So this is a very long answer for a question worth 4 marks. Would it be a good idea to keep the explanation, or to have it strictly math only?
3. ### Solving for the speed of volume

Is this correct?
4. ### Determine what happens to the rate of change of the population over time

So you'll have lim t---> infinite , the function in the denominator will grow faster, so as t grows, P'(x) approaches zero. I believe another way to see this is to note that for t---> inf, P(x)---> 24, therefore reaching a constant value, with zero rate of change. My rate would be zero, right?

6. ### Determine the equation of the tangent line to the function given

sorry, I realized I made an error in my math upon determining the equation. It would be ##y=2x-\frac{3\pi }{2}##.
7. ### Determine the equation of the tangent line to the function given

sorry for the late follow-up, I checked my work again, and my slope is 2. My b value, upon calculation, is ##-3\pi ##. Would my final equation be ##y=2x-3\pi##?

9. ### Differentiate, but do not simplify: ##y=3ln(4-x+5x^2)##

please excuse me horrible writing, it's supposed to be a 4

21. ### Differentiate and simplify: f(x)=sin^2(2x)-cos^2(2x)

yes, sorry, I forgot to include the question! here it is:

23. ### Determine the point on the given curve

So I'd leave my final answer as (0.693,2.772)?

25. ### At what point(s) on the given curve is the tangent line horizontal?

It's always relieving and reassuring when I get a heads up from brilliant tutors online :) Thank you!

31. ### Finding the slope using the method of First Principles

The end is cut off a bit, my apologies; I think this is better. What do you think?
32. ### Differentiate (answers not to be simplified)

Thank you for reviewing my work. I'm sorry for cramming the questions together, will submit separate questions next time!

34. ### Differentiate 𝑦 = (2𝑥^3 − 5𝑥 + 1)^20(3𝑥 − 5)^10

sorry for the late reply, but I think I got it..?

41. ### Differentiate x^2-(3x+1)/(x+2)

Is this correct?
42. ### Calculus and Vectors - Limits and Derivatives

if someone can concur that'd be great; also, is there any way for me to check myself in the future?
43. ### Finding the nth derivative of f(x) = x/(x+1)

Did I calculate this properly?
44. ### Finding tangent lines for 𝑓(𝑥) = 𝑥^3 − 𝑥 + 6

sorry, here's the upright version!
45. ### Is This the Right Way to Do It?

whoops, I believe this is better..?
46. ### Is This the Right Way to Do It?

Is this correct?
47. ### Calculus and Vectors - Limits and Derivatives

whoops, it's supposed to be 65/k. Thank you!
48. ### Differentiate 𝑦 = (2𝑥^3 − 5𝑥 + 1)^20(3𝑥 − 5)^10

I guess I will leave it as it is then.
49. ### Differentiate 𝑦 = (2𝑥^3 − 5𝑥 + 1)^20(3𝑥 − 5)^10

wow, this question can really be solved in one step like that?