If we are traveling in a car around a corner and we drive over something slippery on the road (like oil, ice, water or loose gravel) and our car starts to skid, it will continue in a direction tangent to the curve.
Likewise, if we hold a ball and swing it around in a circular motion then let go, it will fly off in a tangent to the circle of motion.
To find the equation of the tangent to the curve, f(x), at P(a,b):
Step 1: Calculate b, the y coordinate of P, using the equation of the curve.
Step 2: Find the gradient function
Step 3: Substitute a, the x coordinate of P in the gradient function to calculate , m, the value of the gradient at P.
Step 4: Use the equation of a line (y-b)=m(x-a)
Step 5: Sometimes you need to change it to the form:
Depending on what the question asks.
YOUR TURN:
Answer the following questions. Make sure to give the final answer in the form stated.
Question 1
1.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 2
2.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 3
3.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 4
4.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 5
5.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 6
6.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 7
7.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 8
8.
Find the equation of the tangent to the given curve at the stated point, P.
Give your answer in the form y = mx + c.
Question 9
9.
Find the equation of the tangent to the given curve at the stated point.
Give your answers in the form ax + by + c = 0
Question 10
10.
Find the equation of the tangent to the given curve at the stated point.
Give your answers in the form ax + by + c = 0
Question 11
11.
Find the equation of the tangent to the given curve at the stated point.
Give your answers in the form ax + by + c = 0
Question 12
12.
Find the equation of the tangent to the given curve at the stated point.
