I am kind of struggling to understand how the slope is derived in the following problem:
"Find the equation of the tangent line to the curve y = x^2 through the point (7, 49)."
The answer is that the slope is 2x but I don't understand how they got there since there is only one set of points given.
Thank you for the help,
How well do you understand the concept behind differentiation?
is 'the rate of change of y with respect to x'. It is used to tell us the equation of the gradient of the curve at any point.
In the question, . So take any point on your curve. Let's say This has x co-ordinate 3.
Substituting this into gives . What this means is that at the point the gradient of the curve is 6.
Also, I don't think that is the answer to that question.
We have a point (7,49) and we know that . So the gradient of the tangent is .
So we know that when x = 7, y = 14 and m is 14. Substitute this into y = mx + c to find c and you'll find the equation of the tangent.