Finding tangents, given (x,y) information

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In summary, to find h′(2) for each function h(x) given in the conversation, the first derivative is calculated and then the given values are plugged in. This process is repeated for each function.
  • #1
musad
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Stuck on another calculus question and not sure where to begin:

For each h(x) defined below, find h′(2), given that f(2)=−3,g(2)=3,f′(2)=−3 and g′(2)=7.
a) h(x)=f(x)g(x)

b) h(x)=g(x)/1+f(x)

c) h(x)=x^2/f(x)

d) h(x)=g(x)/x^2

Thanks for all your help. Sorry for bombarding but these are the last few that I am stuck on.
 
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  • #2
Question a).
Step 1: Calculate the first derivative
$$h'(x) = [f(x)g(x)]' = f'(x)g(x)+f(x)g'(x)$$
Step 2: Plug in the values $f(2),f'(2),g(2)$ and $g'(2)$.

The others are similar.
 

FAQ: Finding tangents, given (x,y) information

1. What is a tangent in relation to (x,y) information?

A tangent is a line that touches a curve at only one point, and is perpendicular to the curve at that point. In (x,y) information, a tangent is a line that passes through a given point (x,y) and has the same slope as the curve at that point.

2. How can I find the equation of a tangent line given (x,y) information?

To find the equation of a tangent line, you will need to use the point-slope form of a line. First, find the slope of the curve at the given point (x,y). Then, plug in the values for the point and slope into the point-slope equation: y - y1 = m(x - x1). This will give you the equation of the tangent line.

3. What is the purpose of finding tangents with (x,y) information?

Finding tangents with (x,y) information is important in calculus, as it allows us to approximate the behavior of a curve at a specific point. It also helps us to find the slope of a curve at a given point, which can be useful in solving various mathematical problems.

4. Can I find multiple tangents for a single curve with (x,y) information?

Yes, it is possible to find multiple tangents for a single curve with (x,y) information. This is because a curve can have multiple points where it intersects with a straight line, and each of these points can be used to find a different tangent line.

5. Is it necessary to have (x,y) information to find a tangent?

Yes, in order to find a tangent line, you will need to have (x,y) information for a specific point on the curve. This is because the equation of a tangent line depends on the slope of the curve at that particular point, which is given by the (x,y) coordinates.

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