Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AISL
    /
    Differentiation
    /

    Problems

    Edit

    Problem Bank - Differentiation

    Access custom-built, exam-style problems for differentiation. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    Select a Difficulty:

    12 / 34 problems visible - Upgrade to view all problems

    IB: 5
    4

    !

    0 / 7

    The function h is defined by

    h(x)=21​x3−x2+4x−3.
    1. Find h′(x).

      [3]
    2. Determine the gradient of the curve y=h(x) at x=2.

      [2]
    3. Determine the equation of the tangent to y=h(x) at x=2 in the form ax+by+d=0, where a,b,d∈Z.

      [2]
    5

    !

    0 / 13

    Consider the function

    f(x)=x3−6x2+kx+2

    which has a local maximum at x=1.

    1. Show that k=9.

      [5]
    2. Find the coordinates of the local minimum.

      [2]
    3. State the interval on which the gradient of the curve is negative.

      [2]
    4. Determine the equation of the normal to the curve at x=2, in the form y=mx+c.

      [4]
    6

    !

    0 / 5

    Consider the function

    f(x)=x2−5x+6x2+x+k​

    and the following tables of values as x approaches 3 from below.

    x

    2.500

    2.900

    2.990

    2.999

    f(x)

    13.00

    7.67

    7.06

    7.01

    1. State x→3lim​f(x).

      [1]
    2. Explain why f(3) is undefined.

      [2]
    3. Determine the value of k.

      [2]
    7

    !

    Plus

    0 / 6

    Upgrade to Plus to solve this problem
    8

    !

    Plus

    0 / 8

    Upgrade to Plus to solve this problem
    9

    !

    Plus

    0 / 4

    Upgrade to Plus to solve this problem
    10

    !

    Plus

    0 / 8

    Upgrade to Plus to solve this problem
    11

    !

    Plus

    0 / 7

    Upgrade to Plus to solve this problem
    12

    !

    Plus

    0 / 7

    Upgrade to Plus to solve this problem

    Ask Plex AI about problem 4

    Get hints, ask questions, and work through this problem step by step