User interface language: English | Español

Date May 2019 Marks available 4 Reference code 19M.2.AHL.TZ1.H_1
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number H_1 Adapted from N/A

Question

Let l be the tangent to the curve y = x e 2 x at the point (1, e 2 ).

Find the coordinates of the point where l meets the x -axis.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

METHOD 1

equation of tangent is y = 22.167 x 14.778   OR   y = 7.389 = 22.167 ( x 1 )        (M1)(A1)

meets the x -axis when y = 0

x = 0.667

meets x -axis at (0.667, 0) ( = ( 2 3 , 0 ) )        A1A1

Note: Award A1 for  x = 2 3 or  x = 0.667  seen and A1 for coordinates ( x , 0) given.

 

METHOD 1

Attempt to differentiate       (M1)

d y d x = e 2 x + 2 x e 2 x

when  x = 1 d y d x = 3 e 2        (M1)

equation of the tangent is  y e 2 = 3 e 2 ( x 1 )

y = 3 e 2 x 2 e 2

meets x -axis at  x = 2 3

( 2 3 , 0 )        A1A1

Note: Award A1 for  x = 2 3 or  x = 0.667  seen and A1 for coordinates ( x , 0) given.

 

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 —Calculus » SL 5.1—Introduction of differential calculus
Show 36 related questions
Topic 5 —Calculus » SL 5.4—Tangents and normal
Topic 5 —Calculus » AHL 5.12—First principles, higher derivatives
Topic 5 —Calculus

View options