296408
Description
Mind Map by Louise Addison, updated more than 1 year ago
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Created by Louise Addison
over 10 years ago
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L2 Calculus
- Differentiation
- Finding the gradient or
rate of change at a point
(Differentiate, substitute in
the x value)
- Find the equation
of a tangent (Use
y-y1=m(x-x1)
- Find the equation of a
normal (Use
m1xm2=-1 and
y-y1=m(x-x1)
- Find the equation of a
normal (Use
m1xm2=-1 and
y-y1=m(x-x1)
- Find velocity
given distance
- Find acceleration
given velocity or
distance
- Find the equation
of a tangent (Use
y-y1=m(x-x1)
- Find the point with a certain
gradient (Differentiate, set
equal to gradient given, solve
for x, substitute to find y / f(x)
- Find where increasing /
decreasing (Differentiate, solve
f'(x)>0 or f'(x) <0)
- Finding turning
points (Differentiate,
solve f'(x)=0)
- Finding maximums and minimums
(Find equation to maximise or
minimise, differentiate, solve
f'(x)=0 to find where max/min
occurs, substitute into f(x) to find
max or min
- Prove a point is max or min
(Find f''(x), if f''(x)>0 then a
min, if f''(x)<0 then a max, if
f''(x)=0 we cannot tell
- Find max or min
distance (where v=0)
- Find max or min
velocity (where a=0)
- Prove a point is max or min
(Find f''(x), if f''(x)>0 then a
min, if f''(x)<0 then a max, if
f''(x)=0 we cannot tell
- Finding maximums and minimums
(Find equation to maximise or
minimise, differentiate, solve
f'(x)=0 to find where max/min
occurs, substitute into f(x) to find
max or min
- Find where increasing /
decreasing (Differentiate, solve
f'(x)>0 or f'(x) <0)
- Finding the gradient or
rate of change at a point
(Differentiate, substitute in
the x value)
- Anti-differentiation
- Finding the function from
the gradient function and
a point (Anti-differentiate,
substitute in point to find
c)
- Find a point on the orginal cuve
or function (Find original
function, substitute or solve to
find point
- Find velocity
given
acceleration
- Find distance given
velocity or acceleration
- Find a point on the orginal cuve
or function (Find original
function, substitute or solve to
find point
- Finding the function from
the gradient function and
a point (Anti-differentiate,
substitute in point to find
c)
- Sketching
functions
- Sketch function from gradient function
(x-intercepts become turning points,
above y-axis is increasing, below
y-axis is decreasing
- Sketch velocity function
from acceleration
function
- Sketch distance
function from velocity
function
- Sketch velocity function
from acceleration
function
- Sketch gradient function from function
(Turning points becomes x-intercepts,
Increasing is above y-axis, decreasing is
below y-axis
- Sketch acceleration
function from velocity
function
- Sketch velocity
function from distance
function
- Sketch acceleration
function from velocity
function
- Sketch function from gradient function
(x-intercepts become turning points,
above y-axis is increasing, below
y-axis is decreasing
- Kinematics
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