Tangents and Normals - questions
SL and HL
Ques%ons 1 to 5 should be completed without the use of a GDC.
1
2
2
A curve has the equation y = 3x − 7x + 2.
a)
Find the value of y when x = 3.
b)
Find the gradient of the curve at the point where x = 3.
c)
Find the equation of the tangent to the curve at the point where x = 3.
()
A function is defined as f x = 6 + 5x − 2x 2 .
a) Calculate f −1 .
b) Evaluate f ′ x .
c) Calculate f ′ −1 .
d) Find the equation of the normal to f x at the point where x = −1.
( )
()
( )
()
()
3
1 x
Find the equation of the tangent to the function f x = − +1 at the point where x = 1.
x 2
4
3x
Find the equation of the normal to the curve y = 2 x + at the point where x = 4.
4
5
x 3 3x 2
A curve is defined as y = +
−10x + 2.
3
2
a) The curve has two horizontal tangents. Write down the gradient of the horizontal tangent.
b)
c)
dy
Find for this curve.
dx
Use your answers to a) and b) to find the two x values through which each of the horizontal tangents pass.
(c) ibmathsdotcom
Tangents and Normals - questions
6
()
SL and HL
()
A function f x is defined as f x = x 3 + 4x 2 − 6x − 5.
a)
b)
c)
d)
e)
()
()
Find the value of f 1 .
Find the value of f ′ 1 .
Hence find the equation of the tangent to f x where x = 1.
Find the equation of the normal to the function at x = 1.
The normal at x = 1 to f x meets the function again at P and Q.
()
()
Find the coordinates of P and Q.
7
2
A curve has the equation y = 2 − 3x − x .
a)
b)
dy
Find for this curve.
dx
A tangent to the curve is known to pass through 0,18 and −2,8 , and touches the (
)
(
)
curve at the point Q. Find the coordinates of Q.
8
4
Find the coordinates where the tangent to the curve y = + x 2 at the point where x = 2
x
will meet the curve again.
(c) ibmathsdotcom