Finding Derivatives and Using Point-Slope Form

hman24
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Homework Statement



Need help with all of question 8 , any help would be appreciated thanks :D

maths001.jpg



Homework Equations





The Attempt at a Solution


 
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so find the derivative of those functions, and plug in x= whatever point they asked about. that's the slope at that point. so for the first one, find f'(x), and then plug in 1.
 
hman24 said:

Homework Statement



Need help with all of question 8 , any help would be appreciated thanks :D

maths001.jpg



Homework Equations





The Attempt at a Solution


You DO know that the slope of the tangent line equals the derivative, don't you? Well, in 8(i) you have y = (3x^2 - x - 3)^3. What is preventing you from taking the derivative?

The other are all similar: either use derivative formulas you have covered in class, or look in the book for related material that you may not have covered explicitly, or else consult tables of derivatives, etc. Basically, you just need to start.

RGV
 
Do you know how to chain rule?
 
Find the derivative (which is the slope), then use point slope form:
y-y1=m(x-x1)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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