Calculating Rates of Change in Calculus Problems

AI Thread Summary
To determine the equation of a line that passes through (2,2) and is parallel to the tangent line of the curve y=-3x^3-2x at (-1,5), first find the slope of the tangent line using the derivative at that point. For estimating the instantaneous rate of change of a sphere's surface area with respect to its radius at 10cm, recall the formula for the surface area and how it varies with radius. Understanding the derivative will help in both problems, as it provides the necessary slopes. Knowing these concepts will guide you towards solving the challenges independently.
Hollysmoke
Messages
185
Reaction score
0
Our teacher gave us some extra challenge questions and I've solved them all except for two, which has been really bugging me:

1) Determine the equation of a line that passses through (2,2) and is parallel to the line tangent to y=-3x^3-2x at (-1,5)

2) estimate the instantaneous rate of change of the surface area of a sphere with respect to its radius when the radius is 10cm.

I don't want to know how to solve them but just a bit of help to get me along on my own would be nice. Thank you.

EDIT: I just realized I put this in the wrong thread. Is it possible to move it to the Intro Calculus thread? Thank you.
 
Last edited:
Physics news on Phys.org
1) Two lines are parallel if they have the same slope. What's the slope of the tangent line to the curve at the point given?

2) What is the formula for the surface area of a sphere? How would you find how it changes with r?
 
Y may be know that the slope of the tangent is given by the value of the derivative at the pooint (-1, 5) . Knowing the slope, you will be able to determine the equation of the line.

2) You must know the rate of change of the radius.
Do you know how to calculate the surface area of a sphere in function of its radius?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Football Trajectory: Radius & Speed Rate of Change
Replies
16
Views
11K
Rate Of Change Of Current In An Inductor
Replies
6
Views
8K
Calculating Instantaneous Rate of Change for a Quadratic Function
Replies
8
Views
2K
B Mass estimate only through mass rate of change
Replies
4
Views
1K
Calculus Multivariable calculus PDF books
Replies
10
Views
3K
Problem involving the human body and rate of heat transfer
Replies
6
Views
10K
Faraday disc, rate of change of the kinetic energy.
Replies
1
Views
4K
How Do You Calculate Charge and Current Change Rate in LC Circuits?
Replies
1
Views
3K
Finding the Rate of Change of Water Height in a Filling Cylindrical Tank
Replies
11
Views
2K
MHB How to Solve Related Rates Problems in Calculus 1
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top