# Rough estimation of the slope of the curve [closed]

I am very much confused on finding the slope the curve at a specific point on a graph. I know the process, draw a tangent at the point and then estimate $y$ units per $x$ units. I am doing that but it doesn't match with the answer sheet. Different people will have different tangent line with same point, isn't it? My graph is attached. What is the slope at the point P1?

## closed as off-topic by Saad, Brahadeesh, Shailesh, user99914, Ethan BolkerJun 23 '18 at 13:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Saad, Brahadeesh, Community, Ethan Bolker
If this question can be reworded to fit the rules in the help center, please edit the question.

• You should include your work in order for us to help. In particular, what tangent line did you draw? What slope did you get? Also, what does the answer sheet say? – Dave Jun 23 '18 at 4:15
• Not just work. They actual question and answer. What point are you trying to do and why don't you get it right. How the heck are we supposed to know why you got it wrong? – fleablood Jun 23 '18 at 5:37
• Why do you refuse to tell us the answer you got and the answer in the answer sheet? – Joel Reyes Noche Aug 3 '18 at 5:17

Approximations are just approximations. I would say the slope at $P_1$is approximately $-3$
To check my approximation I found the equation for the cubic curve passing through $$(-1,-2), (0,0),(1,2),(-2,2)$$
I found $y= -x^3+3x$ whose derivative at $P_1$ is $-\frac {7}{3}$
Try the calculus method. Take a point $K_1$ near $P_1$ then draw a secant $P_1K_1$. Then take a point $P_2$ between $P_1$ and $K_1$, and draw $P_1K_2$. Continue this process until $K_n$ is very close to $P_1$. It'll be a good approximation of the tangent.